Why do fossils prove that evolution has occurred?

Answer 1

Fossils themselves prove nothing.

However, in comparing fossils from earlier, later and much later times, we see such similarlities accompanied by differences; we see creatures remaining as they were, and then suddenly developing into others, sometimes disappearing, soemtimes living alongside them.

The fossils show us a small picture of basically what was alive at that time. We know that for example, some apelike creatures existed in one place at one time, and then later on they moved "here". Then we see that they start becoming fewer and fewer, while a similar - but different - creature becomes more common. Then #2 becomes rarer while another very similar but different animal becomes more common. And then #3 starts getting less common...

Sometimes at each stage, we find there are several animals which are all different, but all similar to the ones before. Sometimes we only one, immediately replacing its predecessor. As explained by evolutionary theory, this is what we expect, and this is what we see.

Answer 2

The changes seen in the fossil record are not random, inexplicable changes, they fit into the kind of pattern that would be expected to happen as a result of the evolutionary process. Species change in a progressive manner, changes building on previous changes. The fossil record is very complex, and it certainly includes major events such as the extinction of the dinosaurs which was not caused by evolution, but by the impact of a comet, but nonetheless, you can still see evolution taking place. After the dinosaurs became extinct, there were new ecological niches available, which mammals evolved to fill. The fossil record is very clear that evolution has been taking place.