Excellent question, Mia. One thing to keep in mind is that continents haven't always been arranged the way they are today. For example, eastern South America was joined to what's now west Africa as recently as 120 million years ago. Prior to that time, a large lake system sat in the middle of what today are these two separate continents. These lakes slowly filled in with sediments, which in turn became a sedimentary rock formation. (Interestingly, this formation contains the bones of extinct aquatic reptiles call mesosaurs.) As South America and Africa rifted apart from each other, this formation, and its fossils, were divided between the two landmasses. Imagine slicing a pepperoni pizza in half. Some pepperoni pieces will be cut in two. You can move around the two separated pizza halves all you want, but those split pieces will match up again once the two halves are reunited.

Going back to mesosaur fossils, since these animals lived in fresh water, it would have been impossible for them to cross an ocean when they were alive. It makes more sense to conclude that mesosaurs once lived across a large supercontinent, which has since fragmented into pieces.

Much in the same way that there is only one of you, each rock formation is unique, and formed at an individual point in time and space. Because the Earth's crust is broken into several different pieces (tectonic plates), if you were to move pieces of the earth's crust around, you would move around whatever is on top of the crust. So, if a rock formation must have been formed at one singular location, but is now found in two different locations, the crust MUST have been moved.

Dr. Tanya Atwater is a Professor Emeritus at UC Santa Barbara, and she is one of the pioneers of plate tectonic theory. She has some awesome animations which show how the continents have moved throughout time. You can watch one here: plate tectonics animation

Different continents may have similar conditions, which allow similar rocks and formations to form. For instance, the Hawaiian Islands and Iceland are both volcanic and both have a lot of basalt from when they erupted; however, the basalts have different chemistry because they came from different magmas.

The processes that form rocks are the same on any continent as on any other continent. Some processes that form rocks are not even unique to Earth - consider for example the Burns Formation on Mars, which exogeologists at NASA explored using the Spirit and Opportunity rovers!

Excellent question Mia! I study this very question in my research at UCSB.

The quick answer to your question is that the continents are constantly in motion, slowly shifting around Earth's surface, so rocks found on different continents today may have been a single continent in the past.

If you've ever looked closely at the continent shapes, you may have noticed how they seem to fit together like a jig-saw puzzle. The easiest link is between North and South Americas with western Africa and Europe. The concept of "continental drift" was posed by Alfred Wegener in the early 1900's. He thought all the continents once fit together into a single supercontinent whose name in Greek means "all earth", that eventually broke up and moved into their current positions. Early geologists rejected Wegener's hypothesis because he could not provide a mechanism for how the continents could move. Later, Marie Tharp and Bruce Heezen created the first scientific map of the Atlantic Ocean seafloor. Her research revealed continuous rift valleys along the center axis of the Atlantic Ocean, which lead to the currently accepted theory of plate tectonics.

Plate tectonics theory became widely accepted starting in the 1970's, and describes Earth's surface as broken into numerous plates that move around Earth's surface, either slamming into another plate, destroyed under a neighboring plates, or grinding past another plate. The tectonic plates, or slabs of Earth's crust sitting on top of mantle rocks, move as rigid crust on flowing mantle rocks (crust on the mantle is like a graham cracker on a marshmallow, both are solids but the mantle rocks can be deformed plastically like a marshmallow).

The fascinating part about plate tectonics is that scientists now know that Earth's surface has gone through several cycles of crust smashing together into supercontinents and then breaking up into smaller continents.

Therefore, the similar rock types and rock formations can be seen of different continents because those continents were once connected. Earth's rocks record that history of the continents shifting around through time.

These features are part of a collection of evidence in support of the theory of plate tectonics.

The similarity in the rocks (including both the types of rocks and features such as magnetic "stripes"), their layering, fossils found within them, and the fit of large-scale geological features (e.g. coastlines and mountain ranges) spread across several continents led Alfred Wegener to posit that the continents were joined together at some point in their past.

Since the continents are now separated, they must be able to move. This is the continental drift theory.

Plate tectonics is the modern version and is an evolution of continental drift theory. It considers that the crust of the earth comprises several distinct tectonic plates which essentially float on a liquid-ish mantle of melted (but still very viscous, i.e. thick and not easily flowing) rock. Those plates can then move, driven by a variety of forces.