Pathfinder uses spell slots to determine how many spells a character can cast at once. A spell slot is a reservoir of magic that a character can use to cast a spell. Each character has a number of spell slots equal to their Intelligence modifier. A character can cast any number of spells of 1st level or higher using their spell slots.
A character cannot cast a lower-level spell in place of a higher-level spell slot. For example, a 2nd-level wizard could cast either 1st-level or 2nd-level spells, but not 1st-level and 3rd-level spells. The number of slots available to cast a particular spell is determined by the wizard’s class level and the level of the spell being cast. For instance, an 8th-level wizard with the Wizard Spells Known feat can cast any 1st-, 2nd-, 3rd-, or 4th-level wizard spell in place of a 1st-level or 2nd-level slot. .
A character’s total number of spells per day is determined by the character’s class level and his intelligence modifier. A wizard with an intelligence score of 12 can cast four 1st-level spells per day, two 2nd-level spells per day, and one 3rd-, 4th-, or 5th-level spell per day.
Pathfinder uses an energy system similar to that used in D&D 4e called “mana points.” Mana points are used to power spells and abilities. A character starts with a certain number of mana points (based on their class level) and gains more mana points as they level up.
Characters must expend mana points to use abilities and spells, just like they must expend energy when casting regular magic in Pathfinder. Mana points are regained at the rate of 1 point per day, so a 4th-level wizard would have 4*(1+Int modifier)/8 mana points available at any given time.