Wizards, Alchemist, Magus, Investigators, and witches all have a book (or familiar) of spells that they add to as they level and these are their "spells known"
Clerics, warpriests, rangers, shamans, paladins, and druids get all the spells as their "spells known"
Both of these groups are Prepared Casters, each day they have to prepare which spells they want to have ready for the day and they pick from their spells known. So if you wizard has 4 lv1 slots and you fill them all with magic missle, that's the only spell you can cast. If you fill 2 with magic missle you can spend a half-hour to prepare the other 2 spells with any appropriate level spell you know. These guys often know more spells then they can cast in a day.
Spontaneous casters such as the Bard, Oracle, Sorcerer, Summoner, Bloodrager, hunter and skald have a table that tells them how many spells they have as "known spells" and they can cast any spell known whenever they want as long as they have slots available. So if you're a sorcerer and need a spell, if you know it you can cast it. These guys often know less than they can cast.
The arcanist is different in that he has a book of spells known like a wizard, and then in the morning he picks some to be his spells known for the day like a sorcerer and then can cast those spells through the day as if he was a sorcerer who had those spells as their spells known.
Clerics, druids, Magus, Paladins, Rangers, Shamans, Warpriests, and Witches all prepare spells. Divine prepared spell casters know all the spells on their spell list, but still have to prepare them. Arcane prepared spell casters can learn an any spell from their list, but have some way of recording their list of spells known.
All spell casters prepared or spontaneous have a limit to how many of each level spells they can cast per day. This number increases as you level up.