What Looting changes
At Looting III, common drops increase by up to one extra item and rare drops get a substantial chance boost. Wither skeletons with Looting III drop significantly more wither skulls, and most mobs yield extra gunpowder, arrows or pearls — which is why a Looting sword is standard equipment at any mob farm.
The three levels
Looting I slightly raises drops, II improves the rare-drop chance further, and III is the maximum in vanilla survival. Looting does not affect experience from the kill (that is separate) and does not work on players.
What it does not affect
Looting has no effect on blocks, on fishing (that is Luck of the Sea) or on experience. It applies to mob loot only, so pair it with a farm that spawns the mob whose drops you want.