Darwin examined remains of extinct organisms while on his journey. The remains had been preserved in rock for a very long time. What are these remains called?

The remains are called fossils. Fossils are remnants of animals, plants, or microorganisms that have been solidified in the process of fossilization, where the organism is surrounded by sediment, minerals, and other solid objects which are compressed and heated around the organism over time. This forms a solid mass with the preserved organism inside, other known as a fossil.