I think this is easier that some of you are making it out to be. Consider a road that runs northwards and splits into two roads. One goes NW - half left. The other goes NE - half right. Stop briefly in the intersection. You have a choice: you can go this way, or that way, or the other way. There are three paths you can choose from. In this context, the word "way" has to do with the path of travel.
The concept is similar for a 3-way switch. Some of you have said essentially the same thing. But talking to a customer in terms of terminations is harder for them to follow. Talking about roads is likely a bit easier for them to understand.