There's no trick to the meaning of overseas. If someone goes overseas, they've gone "over" the "seas" — to a foreign country.
When overseas came into use, there were no airplanes, so technically speaking, one traveled "across" or "on" the seas, in a ship. Nevertheless, one was thought to have made it "over the sea," hence overseas. When traveling overseas, make sure your phone works on the network in the country where you're headed. Also, the laws and customs overseas can be very different from the ones we have here, so be careful. What here at home you consider small potatoes legally might be a big deal overseas.