Fossils can be dug out of holes in the ground on your island, or other islands you visit. Blathers can assess the Fossil to find out what it contains. There are 73 fossils to find and donate.
This page lists all of the different fossils, along with their sale price in bells. The un-assessed Fossil is only worth 100 bells, while assessed fossils are worth between 1,000 and 6,000 bells.