Hardpoints are primarily used to limit the weapon loadouts of ships.

Turret Hardpoints can mount guns like Lasers, Blasters, Artillery, etc.

Launcher Hardpoints can mount missile launchers such as rocket launcher or heavy missile launchers.

CCP uses them to add flavor to ships along with the bonuses. For example the Drake has 8 high-slots, 7 launchers hardpoints and 0 turret hardpoints. So our Drake can fit missiles but no guns and it will have an 8th free "utility" high slot.

Some ships like the Tristan have split weapons, in the case of the Tristan, 2 launcher and 2 turrets for 4 high slots. So it can only mount 2 blasters and/or 2 missile launchers. This keeps the Incursus (3 high slot, 3 turret, 0 launcher) relevant as a pure blaster frigate. Without hardpoint everyone would fly a Tristan with 4 blasters exclusively.

Upgrade hardpoints is the official name for rig slot, so not really related to the turret/launcher hardpoints.