mutiple reasons (some already given):

1. height: it's easier to get in and out of a bed, if it's higher up (about sitting height)

2. insulation: a mattress with direct contact to the floor will cool out faster than one in the air (depending on the type of floor)

3. friction: the mattress might move around when just put on the floor. a bed frame is more likely to stay where it is (not a big problem, but it can be annoying)

4. comfort: the slatted frame at the bottom adds another layer of flexibility, so the bed can adjust to your bodies contours better.

5. ventilation: when you sleep, you sweat. that moisture goes into the mattress and during the day it vaporizes out again. this works better if the mattress is surrounded by air on both sides. (it's also why bed frames with a solid floor are less good than those with a slatted frame)

edit forgot 6. storage (thanks u/sugarcanejane for reminding me)

edit2 since people keep mentioning it: 5. includes little creepy crawlies resulting from a mattress soaked in sweat and other stuff from the body loses during the night (skin flakes, etc.)