Here’s how it will work: Person A has their Steam Library. Person B requests access to Person A’s Library. Person A grants access, and now Person B can play any game from Person A’s library, and will even earn their own achievements and make their own saves, and presumably, earn their own Steam Trading Cards.
Here’s the caveat: only one person can access a Library at a time. So if Person A wants to play something from their Library, even if it’s a different game than what Person B is currently playing from it, Person B will be told they need to save and quit, or purchase the game if they want to keep playing.
It’s unclear right now how this will all interact with Steam’s Offline Mode, but I’m assuming that if you share your Library and go offline, it will no longer be shared, or if you try to play something while offline, you’ll have to go online to be able to play (so Steam can kick off your moocher).
Obviously, Steam Family Sharing is there for convenience, and for families/couples. If Dad is at work, the Son can now play any game from Dad’s library without Dad having to hand over his login/password. Son even has access to all the DLC Dad bought. Or couples who work at different hours, and want to try each other’s games without having to buy their own copy. What Steam Family Sharing is not, is a one-stop shop for moochers, since that wouldn’t really help Steam sell games.