Wow TruthDoubter, you have quite a hostile crowd here. I wonder what you did to get everyone so riled up?
No matter, let's start with the basics of what evolution is. Evolution is a scientific theory that explains the diverse speciation we observe on our planet (in other words, it explains why there's so many different kinds of life forms). Much like Atomic Theory explains how matter is made up of discrete units (atoms) the Theory of Evolution explains how species change over time.
The nuts and bolts of evolution are that genetic mutation along with selection slowly change a species. This is because animals* that reproduce pass on their genes. And animals that don't reproduce don't pass on their genes. Some animals within their species will be better a reproducing and thus their genes will spread more. Over time, the genetic material that gave them that animal an advantage will spread throughout the whole species.
Now, to go slightly deeper, we can look at the two mechanisms of evolution. The first is mutation. Genes are never copied perfectly. Thus the offspring of an animal will always have slightly different genetic material from its parent(s). Sometimes this new genetic material puts the offspring at a disadvantage and the offspring isn't able to reproduce - so the "bad" genes will not be passed on. Sometimes the genetic material has no discernable effect - so the offspring is able to reproduce just as well as its parents. And sometimes the genetic material gives the offspring an advantage - in which case it's able to produce more offspring. And those offspring will also have that genetic material that gives them an advantage so they too will reproduce more offspring. Etc. Until the whole species has this new mutation.
The other basic component of evolution is selection. This is broken down into three types:
1.) Natural Selection. Animals that are better suited to their environment are more likely to survive. And animals that can survive can reproduce. While animals that can't survive in their environment will not reproduce.
2.) Sexual Selection. Animals that that are able to attract a mate are more likely to produce offspring. And animals that can't attract a mate won't reproduce offspring.
3.) Artificial Selection. Animals that have desirable traits are more likely to be selected to produce offspring. Whereas animals with undesirable traits are less likely to produce offspring.
So the mutation provides new features to the animal and the features that are advantageous are "selected" by one (or more) of the above processes. Thus, species change over time.
Sometimes a single species in two separate environments will drift apart genetically as genes selected for in one environment are not selected for in another. If the two groups of the species become isolated from one another for long enough their genes will diverge so much that the two groups are no longer able to produce viable offspring together. We see this going on with Tigers in Asia and Lions in Africa. They used to be one species but since the continents split Lions and Tigers haven't been able to share genetic information. And what was used to be one species is now two species. And mating between them produces sterile offspring.
If you take away only one point from everything I've written please let it be this: Individual animals don't evolve. Species evolve.
Well, I think that's a good start. Perhaps someone else would like to take it from there. If you have any questions feel free to ask on this thread of PM.
*I'm using the word "animal" to signify a single individual of a species and not a taxonomic group.