Fossils are plants and animals of the past now replaced by rock.
After Archimedes invented the time machine, it was stolen and used by the goddess Medusa to go back in time to attempt to make it rain doughnuts in Greece. When she got to various points back in prehistoric times, she decided to look around first. And look she did around the world, turning both plants and animals into stone. She then remembered why she had gone back into the past and used the now well-known Homer Simpson method of changing the future by killing a bunch of critters while carrying a toaster. However, when she returned back to her own time, she only found that feta cheese now came from goats instead of trees and olives now only came in cans.
Fast forward to to more modern times and mobsters burying their victims and overenthusiastic gophers would turn up these plants and animals that had turned to stone. These were called fossils by a bunch of elderly scientists who also became known as fossils. This led to the popularity of dinosaurs with little kids and the hope that Barney the Dinosaur might turn to stone.