Honey Gather has no effect during battle.
Outside of battle
A Pokemon with Honey Gather may collect Honey after a battle if it is not already holding a held item, similar to Pickup. The chance for a Pokemon with Honey Gather to pick up Honey depends on its level, starting at 5% if the Pokemon is between levels 1 and 10, and going up by 5% every ten levels, ending at a 50% chance from levels 91-100.
Pokemon Mystery Dungeon
In Pokemon Mystery Dungeon, Honey Gather will increase the chance of finding Nectar in treasure boxes.
Pokemon with Honey Gather