and finally a description of the theory of evolution.
I use the word description advisedly. You can't "define" a theory. It is too big and complex for that.
Since we are going to discuss the theory of evolution we'll take as given the data that needs this theory to explain. There's a ton of that and you don't seem to want to start that far back.
So the problem that Darwin was faced with is that the living things on earth had changed over time. How could this come about?
He put together two concepts. One is that living things do not reproduce exactly. And from Malthus he realized that in the long run not all thing born will be able to live to reproduce.
Putting these together we realize that there are things which influence which individuals do reproduce. A lot of it will be just dumb luck (the tree did or didn't fall on you) but that averages out in the long run. If individuals are different from each other then sometimes (maybe not often and certainly not all the time) that difference will enable one individual to reproduce and another one not to.
Repeat this with a few billion individuals of different creatures alive at one time and then repeat that some 10s or 100's of millions of times and large differences could result if the environment allowed for the changes to be useful.
That's the basic idea. Darwin needed some mechanism within a living thing that could allow for changes from one generation to the next. He had no idea what it would be.
He emphasied that gradual change could do the job (he may even have said that was the only way it would happen I don't remember)
He developed this idea after looking at a lot of extant living things and seeing the relationship between them. I can't find my copy of "Origin" right now and don't remember if he used any fossil evidence at the time. He was aware of the existance of obviously extinct fossils though. There wasn't all that much available in any case.
This gives the basic theory. Then it had to undergo the beginings of a century and a half of examination and testing against new discoveries.
A couple of huge areas of new information that support the theory are, of course, genetics and many, many more fossils. Both are exactly what the theory needed to underpin it and that it predicted would exist. The details have been filled in with methods that would have been deemed impossible in Darwin's day. Perhaps most noticable accurate, absolute dating of geologic structures. All that Darwin had was relative dating with guesses for the time periods involved.
The genetic information has enabled us to see that relatively rapid changes are possible due to the kind of effects that even a few genetic changes actually have on the phenotype (what the animal looks like). They have also allowed us to see a trace, a hidden record if you will of the changes.
The fossil information has filled in a bunch of transitional forms between major groupings. Amusingly the bird-reptile connection was found very shortly after Darwin finally published. Many more have come along since.