The A can stand for a verse or a chorus, and could include the pre-chorus as well; basically it's just a segment of the song that sounds kind of the same every time it's played. Verses always have similar or identical musical rhythms but the words change each time, choruses are completely identical, and the pre-chorus is just what leads up to the chorus.
The B is sometimes called the bridge; it's an extra part of the song that sounds completely different from the A part.
Intros and outros can be added onto either end of the basic AABA format, these are just used to improve the flow of the song either by introducing it or ending it.
for example, in the song Make Me Wanna Die by The Pretty Reckless, the verse and chorus (everything from "Take me I'm alive" which is the beginning of the first verse, to "Every time I look inside your eyes, make me wanna die" which is the end of the chorus) is the A; the extra chunk near the end ("I'll die for you my love") is the B; and then it goes back to sounding like A again ("Every time I look inside your eyes" etc, it's not a repeat of the full chorus, but it relates back to it).
Hope that helps you out :)