I surmise that "Ban" means village or small city and "Wat" means temple, but what does Amphoe mean? Is it the district a city is located in?

Yes, it means district. Guess you could compare it with a county in the US.

Changwat - province

Amphur - district

Tambon - subdistrict (administrative level)

Amphur Muang - main city district

//edit - List of Districts sorted by province

Thanks for that info, Twais. I'll mark it down and save it. I suspected it was something like that because my map is covered with Amphoe this and Amphoe that. When I'm driving I often see the word "Ban" before the name of the town, but it could be a small village or a much larger town that is almost the size of a city.

When I'm driving I often see the word "Ban" before the name of the town, but it could be a small village or a much larger town that is almost the size of a city.

A previous topic on that here > http://www.thaivisa.com/forum/Bang-t25156.html

Definition > house; home; place (or one's place); village

Since you are familiar with Chiang Mai (an OTOP village) > Baan Tawai Village