The PDF bit means that if you buy it, you also get a link to download that same book in pdf format. So you can read it on your computer, before it's shipped, if you forget it at home or something. And obviously, you'd want to print copies of the playbooks (character sheets) without cramming your book in the scanner.
The genre is Post-apocalypse, meaning after some major disaster that destroyed society, the earth, or (most likely) both. The book doesn't contain much info about exactly what the world looks like, because the group is supposed to create it in play. It's part of character generation and play – building the world as you go along.
It does support campaign play, though a word of warning since you talk about adventures and campaigns: the MC (AW's term for GM) does not have an adventure or a story prepped. No pre-bought adventure books, no home-made campaign notes, nothing. It's improvised. The MC is allowed to prep some, but never in a "this is what's going to happen" way. Only things like "these guys live over here" and "this is what will happen if no-one fixes the water system".
What happens to the characters is that they're trying to get by, survive, and, if they seem to be doing that, starts striving towards their goals. You might have a group with a travelling gunlugger, the chief of a tribe living in a bunker and his weirdo psychic right-hand man. Then most of what happens would be focused around the bunker and its surroundings. There aren't much dungeon crawling or plain "adventuring" – everyone's supposed to make their characters behave like real people would in this kind of world. Badass, competent people, but real.
Hope it helped. Someone who's played it more can probably give good examples about what kinds of things happen in play.