Fossils tell us where animals and plants used to live, and many animals and plants live only on a single continent. Thus, if we find fossils of a plant or animal on multiple continents, then one likely explanation is that those multiple continents used to be joined together in a single continent.

Fossils provide support for continental drift more or less by the same fossils being present on widely separated continents.

Consider the ways which anything can move around the biosphere. Something could walk across the land, swim/drift through the water, or fly/be blown through the air. Since some continents are widely separated by oceans, walking between them is impossible (e.g. North America to Europe). While some dinosaurs may have been able to swim or fly across the oceans, fossils of land-based dinosaurs which definitely could not have made such sea/air journeys indicate that it was possible to travel across land between the continents. Since this is not possible now, but was in the past, the conclusion is that the continents were much closer together or even connected at an earlier point in time and have since drifted apart.

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First let's talk about continental drift -- this is a theory that the continents are moving. The continents move because of the tectonic plates they sit on. Using GPS, we can actually measure how fast a continent is moving, but before we had GPS, how did scientists know? How could they tell that Antarctica wasn't always at the bottom of the planet, covered in ice? How did they know that Canada used to be at the equator, with sunny tropical weather?

One method of proving that the continents have moved, is using fossils. Now let's talk about fossils. Fossils are the remains of animals or plants that used to be alive. If I find a fossil of a tropical plant in Antartica, then I know that when the plant was alive, this spot on Earth was warm and tropical. This is how fossils can prove that continents are moving.