A point-to-point fare is one-way between 2 cities, but does not have to be non-stop or direct. In your example you are traveling 1-A-2 and it is the fare from city 1 to 2. The fare from city 1 to A and A to 2 is irrelevant (and may be higher or lower than your fare). Stopovers may or may not be allowed -- this varies with the specific fare, and has nothing to do with being point-to-point (generally a stopover is not allowed, a 2nd point-to-point fare is used instead).

Most people do not buy point-to-point fares -- they buy round trip fares. But any trip can be constructed from a series of point-to-point fares. One reason to do this is because fares vary by point of origin. E.g. JFK-LHR-JFK as a roundtrip fare will be different than JFK-LHR at point to point fare, which in turn is different from LHR-JFK. Finding the lowest fare is quite complex.

Lots of other fare types exist. Often the metric for deciding whether a fare is good is comparing it to the point-to-point fare for the same trip, hence the frequent mention of this fare type.