Fossils, the remains or traces of ancient living things, are preserved in sedimentary rocks, rocks that form the recycled fragments of other others. The remains of organisms sometimes getting buried in sediments (such as mud, sand, gravel) after their demise. Given enough time and the right conditions, those sediments are transformed into sedimentary rock, and any biologic material they contain turns into a fossil.

Since sedimentary rocks occur on every continent, it's not surprising that fossils are found globally. Bear in mind, that not all fossils are the same age, and that the continents weren't always arranged as they are today. Therefore, what kinds of fossils we find where is a complicated story. These complications explain why, for example, it's nearly impossible to find dinosaurs in California.

Thanks for an interesting question!

Continents have changed their positions throughout Earth's history due to plate tectonics. When we find the same types of fossils from the same time on different continents, it is often an indicator that the continents were connected at that time. Alternatively, if we find very similar fossils that are not quite the same, it is possible that both continents had similar environments and that two different species separately adapted to those environments with similar results. This is known as convergent evolution.

Different animals and plants live in different parts of the world. You know this already: deer live in North America and northern Eurasia, elephants live in Africa and in southern Asia, and kangaroos live in Australia. When an animal or plant dies and gets fossilized, it gets fossilized in the continent where it lived and died. As a result, the paleontologists of the future will find fossils of deer in the northern hemisphere and fossils of kangaroos in Australia.

The same was true in the past as well.
Tyrannosaurs lived in North America. They did not live in South America. South American fossils of that age include different kinds of dinosaurs, but not tyrannosaurs, because they did not live there.

Of course, the continents themselves move, too. It is possible now to walk from North America to South America, but not in the days of tyrannosaurs; South America was an island continent then, much like Australia is now. Meanwhile it was possible to walk from Australia to Antarctica then, because they were part of the same continent. This means that the animals living in Australia and Antarctica then are found in both continents, since they were the same even though the two continents today are separate.