There are TPDs for places other than PAR, it's just one of the most common ones (ATL is also common). They're generally useful if you have to take a somewhat indirect routing. The most amusing TPDs I've found on a published fare are LON-YHZ, which includes (or at least did recently) a 1200-mile TPD for travel via BOS and a 900-mile TPD for travel via JFK.

You get a stopover and an open jaw and up to eight segments. (This may be up to four each way instead of up to eight total. I've never been clear on that.) If you're making an international connection, the layover can be up to 23:59 in length, so if you wanted to get a quick look at AMS or CDG, you could do so. You can do that as many times as you want. However, if you need to do something like FAR-MSP-DTW-CDG, the connection in MSP is a domestic connection subject to the four hour maximum as far as I can tell.