They found fossils of a land reptile over two continents. Also, they found out that all the continents fitted perfectly like a jigsaw puzzle.
Land reptiles cannot swim therefore finding fossils of the same kind of reptile meant that the continents had to be stuck to one another. The coast of different continents fit like a puzzle.
The discovery of the Mid Atlantic ridges
During world war II submarine warfare, revealed that there were Mid Atlantic ridges that were places where the earth was splitting apart.
At the Mid Atlantic ridges there are volcanic vents and even active volcanos in Iceland where fresh lava, magma is rising from the underlaying mantle. Also there are alternating magnetic strips on both sides of the ridge, that reflect each other. This gives evidence that the earth is splitting apart creating new crustal plates.
The discovery of the Mid Atlantic ridges opened up the issue rejected in the 1920s of Continental Drift. The evidence for Continental Drift was reexamined and combined with the evidence of the Mid Atlantic ridges the idea the continents had at one time been connected was accepted.
The revised theory proposed that the separation of the continents had happened more slowly than in the original theory. The concept of convection currents in the mantle was added to provide a mechanism for the separation of the continents. The revised theory was renamed plate tectonics instead of the original Continental Drift.