evolution: a change in the frequency of alleles in a population from one generation to another.

That's it.  Period.

What does this mean?  Genes, molecular markers, phenotypic characters, etc. often have alternate states.  "Evolution", by definition, is merely a change in the frequencies of those alternate states (for instance... genes coding for eye color) from one generation to the next.  

One problem we have is that many dictionaries incorrectly define "evolution" as follows:

Evolution: The gradual and continuous process by which the first and most primitive of living organisms have developed into the plants and animals of today.

This dictionary definition is not the working definition of evolutionary biologists, and it never has been.  Creationists often incorrectly use this as their starting point, and then point out that some evolutionary biologists believe that evolution is not "gradual" or "continuous" but rather proceeds in "jumps and starts"... a theory (ultimately called punctuated equilibrium) made popular by the late S. J. Gould.  

They then conclude, "See!  Evolution as defined by Webster is untrue!  Even evolutionary biologists don't agree whether it is 'gradual' or 'continuous'. Therefore why should we believe them?"
(Another aside... this definition uses the term "primitive organisms" (a term evolutionary biologists do not use) and only includes plants and animals, negating 3 entire kingdoms of life out there!)
see the following for a discussion of defining "evolution"
http://www.talkorigins.org/faqs/evolution-definition.html

see the following link for "punctuated equilibrium" discussion.
http://www.talkorigins.org/faqs/punc-eq.html

-------------------------------------------

(intro paragraph here mostly stolen from
http://www.talkorigins.org/faqs/evolution-fact.html )
"When "laypeople" talk about evolution they often confuse two different aspects of the definition. On the one hand there is the question of whether or not modern organisms have evolved from older ancestral organisms or whether modern species are continuing to change over time. On the other hand there are questions about the mechanism of the observed changes... how did evolution occur? Biologists consider the existence of biological evolution to be a fact. It can be demonstrated today and the historical evidence for its occurrence in the past is overwhelming.  However, biologists readily admit that they are less certain of the exact mechanism of evolution; there are several theories of the mechanism of evolution."

How does evolution proceed?  Remember, evolution is a change in allele frequencies of a population from one generation to another... so what needs to happen in order for that to happen?  There has to be variation in gene/allele frequencies to start with?  Where does that variation come from?  Mutation.  This is a fact.  All variation in modern (and historical) populations come from mutation.  Some mutations have been demonstrated (in many many MANY organisms) to be either negative (reduces the ability of the organism to either live or reproduce), neutral (doesn't affect the organism), or positive (increases the ability of the organism to reproduce).  The fact of mutation has been overwhelmingly demonstrated.  The fact that mutations have a variety of fitness effects has been overwhelmingly demonstrated.  Where does that now leave us?  Mutations are the ultimate source of variation in populations (FACT).  Variation is necessary in order for evolution to occur (as defined).  The FACT of evolution, that mutations are introduced into populations each generation, and that selection (or genetic drift) can result in the increase or the decrease of those allele frequencies from one generation to the next.  The FACT of evolution is easily demonstratable... mutations happen which result in new alleles.  Allele frequencies change.  Period.

At this point, creationists have started to "smarten up" and they have slipped two new words into public debate (not really used by evolutionary biologists, by the way)... the concept of "microevolution" and "macroevolution".  (This is a VERY recent phenomenon, by the way... and some peop) They say, "Oh, SURE that happens in MODERN populations!  I can understand that MICROEVOLUTION happens!  But all that randomness can't create a human eyeball! (I'm not making this stuff up).  That's MACROEVOLUTION, and God did that.  

At this point, it's pretty clear that such devout people "will never be convinced of the "facthood" of (macro)evolution by any logical argument and I believe it's a waste of time to make the attempt. The best that we can hope for is that they understand the argument that they oppose. Even this simple hope is rarely fulfilled."  (a stolen quotation from above).

It is interesting to note that EVOLUTION is absolutely NOT the same thing as the "Origin of Species".  Evolution is merely explaining how a population gets from one genetic (or physical/phenotypic) state to another.  The "Origin of Species" question is a subset of evolutionary debate... which I can go into at a later date if there is interest.

It involves a population being separated into two geographically separate populations that don't comingle.  "Evolution happens" in each of the populations, (they go on separate trajectories) and when they come back together, they have evolved the inability to reproduce with one another.  This is demonstratable in relatively recently-diverged species.
-----------------------------

So, that's a brief primer on evolution.  Evolution, as defined by biologists, is a FACT.  There are also several "THEORIES" about evolution.  

A commentor wrote earlier, "I keep hearing about how evolutionary scientists have repeatedly debunked the creationist claims, yet I never actually see any evidence of this.  Is there any good information out there for this?"

First off, the question is not really a good one.  Evolutionary biologists do not spend their time (maybe they should spend more) "debunking creationist claims".  This debate was really over with in the scientific community literally over 150 years ago.  (Yes, there are a few "scientists" who argue for intelligent design... however, you will also note that if you look up the publication history of every one of those "scientists", they do not publish on the subject of evolution in peer-reviewed journals.  They publish non-peer-reviewed books or articles written for the masses.  There is no debate over the "fact" of evolution by evolutionary biologists... and even those "scientists" who publish for the masses about ID... they "believe" in "microevolution" (plus, it is also interesting to note that none of them are evolutionary biologists by trade.  They make their living in other fields.))
So, Evolutionary biologists do not sit in the ivory tower "debunking creationist claims".  They sit in the ivory tower trying to figure out patterns in the evolutionary process.  Most specialize on very minute subjects, (What's the evolutionary history of such and such family of organisms?  Does evolution proceed mostly through selection or drift?  How do new species form? Allopatricly or Sympatrically?... The question is never, with evolutionary biologists, "Did god do this?  or did evolution?"

That said... a GREAT resource for "the masses" is
THIS PAGE
http://www.talkorigins.org/origins/faqs-evolution.html
this is excellently written... and will take days to go through, but it's well organized.

------------------------------------------
Back to the original statement that pissed me off...

"Little of DIRECT practical importance would change if either side was ultimately and overwhelmingly victorious in the evolution/creationism debate."

This is absolutely untrue.  First off, evolution has won in the scientific community.  Period.  There is no debate on the fact of evolution.  It would be a horrible travesty to teach our children that there is really a debate on this subject by those who actually study it.  It just isn't there.  The only thing keeping this debate alive is religious people who cannot reconcile the fact of evolution with their religious beliefs.  This is not be the fault of scientists.  There is no place whatsoever in a science classroom for "ID" or "Creationism".  These PHILOSOPHIES should be discussed elsewhere, lest they be given the slightest bit of credibility.

So, what has the study of evolution given to "the masses" of practical importance?

First off, (and I truly believe that this is one of the most important reasons to study evolution).  

KNOWLEDGE!  Where did we come from?  Where are we going?  Where did the vast history of life on earth come from?  How did life begin?  How do species arise?  How do they go extinct?  How do species evolve?  THESE QUESTIONS ARE IMPORTANT FOR KNOWLEDGE'S SAKE!  Why are we going to the moon?  Why are we going to Mars?  Why did we build a space station?  Why do we map the ocean floor?  Why do we build telescopes?  KNOWLEDGE!  Knowldedge is important...

That said, a very influetial biologist once said, "Noting in Biology makes sense except in the light of evolution."  T.H.Dobzhansky.  and this is absolutely true.

Studies of any biological process only make sense in an evolutionary context.  Evolutionary theory revolutionized the way all fields of biology think and understand their fields... molecular biology, Ecology, Forestry, Animal Husbandry, marine biology, etc. etc. etc.

What about practical results of evolutionary biology?

Evolutionary biologists discovered DNA.  It was evolutionary biologists who were interested in this ultimate source of variation...  Thanks to evolutionary biologists, we can now perform forensic science.  We can perform gene therapy (or are beginning to).  All modern animal and plant breeding programs use basic evolutionary principles (and tools created by evolutionary biologists... QTL analysis and many other  genetic tools) to breed better crops and farm animals.  Evolutionary biologists have discovered the origin of most crop species due to evolutionary techniques, and breeders are now going into those original crops to find novel sources of variation to introduce into existing crops...

MEDICINE!  Without an understanding of evolution, the thought of developing new antibiotics would never have happened.  The FDA recently banned the use of some antibiotics in chickens.  Why?  Because microbes are EVOLVING resistence.  The center of disease control... The CDC is using evolutionary techniques to determine how disease organisms jump from host to host.  Where that might happen and when, and what can we do to stop it?.  AIDS research.  The "drug cocktail" used to treat AIDS cases was developed due to the recognition that the AIDS virus was developing resistence to individual drugs... ETC. ETC. ETC.

Saving endangered species (defining minimum viable populations by the EPA)!  Zoo-animal breeding!  Cloning!  Gene therapy, Transgenic crops (whoops!) (and possible consequences all made possible thanks to evolutionary biologists.

This is not trivial.  It is important to not let creationists set us back.  Evolution has won.  The practical results of this would just be too devastating to all fields (medicinal and biological) that work with living organisms.