There are abundant fossil records that indicate continental drift. Many unique fossils are found on continents on opposite sides of oceans, which suggests the continents did not have an ocean between them initially. Certain types of extinct land animals, like cynognathus, left fossil remains on South America and Africa. Since they were land animals, the cynognathus could not have swam across an ocean of water that now separates South America and Africa.

Some ancient plants also show patterns across “matching” parts of continents. The remains of one type of ancient plant, glossopteris, are found on South America, Africa, India, Antarctica, and Australia. There is no likely chance that this plant migrated across oceans of water to distribute its population so widely. Hence, these continents must have been joined together when glossopteris were growing.

The list of evidence is so vast that I can't possibly explain it all here. The most direct evidence is that we can measure continental movement directly using GPS, but we've known that continents move for much longer than we've had GPS.

and see that the ocean spreads out from spreading centers at the mid-oceanic ridges. This means that the continents have to move as they are pushed around by the mid-ocean ridges.

There's a lot more evidence beyond this, too - the fact that all of the continents fit together if you place them on a map, the fact that fossil species' ranges can be found spanning continents that don't today touch, and more.