A wastepaper basket is a container in which to collect trash. Most rooms at Hogwarts have at least one wastepaper basket. Peeves like throwing them at people’s heads (PS8).
In Number Twelve Grimmauld Place, an enchanted wastepaper basket in the room used by Harry and Ron swallowed paper thrown its way, then burped loudly. Later it coughed up owl droppings (OP9).
Peeves threw chalk into one when he was kicked out of a room by McGonagall (PS9).