The tectonic plates (effectively the crust) float about on the mantle and bang into each other. This is what causes earthquakes. I’m writing this in Noddy-speak so apologies if you feel patronised!
There are several sorts of joins between plates. These are:
Ones where they rub along (like the join that is the San Andreas fault in California)
Ones where the plates are drifting apart and magma is welling up between them, making new crust (mid ocean ridges like the one that runs through Iceland)
Ones where one plate goes under another (subduction zones, like the Marianas Trench)
During the late Silurian and early Devonian periods (about 400 M years ago) the plate that is now N America bumped into the plate that has our bit of Europe on it. Some of America broke off and stuck to Europe. The join roughly follows the Scottish/English border.
I might have a few details wrong, but essentially that’s about it.
It was recognised as such both by a comparison of rock types, tracing the Geat Glen Fault to similar structures in N america and also the presence of fossil ammonites that could not traverse deep water in rocks in N America and Scotland, and an entirely different type in Northern England, implying that these two areas where once seperated by a substantial body of water.
If you look at the map on this page
http://www.fettes.com/shetland/Northern_Isles/geological%20evolution.htm
the join between what was once America (the Laurentian supercontinet) and proto-Europe is along the line marked by the Iapetus suture, Iapetus being the name given to the proto-Atlantic.