The Banishing Charm is a spell used to send an object away from the caster. The spell with the opposite effect is the Summoning Charm.
 Effects and Limitations
The Banishing Charm is a fairly difficult spell to cast and is not taught until students' fourth year at Hogwarts. The class has to read three extra books in preparation for lessons on the Summoning Charm which they learnt first.
Assuming the spell works in a similar way to the Summing Charm, it requires the caster to concentrate on the object as well as to speak the incantation. If the witch or wizard isn't concentrating enough the spell wont work and objects either wont move at all or will give up partway through.
It takes practice for the spell to send the object in the direction that the user wants it to go.
 Uses in the books
 Fourth Book
Harry Potter was taught the Banishing Charm in Charms Class by Professor Flitwick. They were taught using cushions rather than trying to banish objects around them, as solid objects flying around was something of a safety hazard. Unfortunately Neville Longbottom's aim was so bad that he kept hitting Flitwick with the banishing spells and sent him flying around the classroom, rather than the cushions. Hermione Granger and Harry Potter were both able to cast the spell properly however, and send the cushions into the box they were meant to be aiming at. Ron Weasley was less accurate and knocked Parvati Patil's hat off with one cushion, sent another into a chandelier and yet another out of the window.
 Additional Canon
In the video game Harry Potter and the Prisoner of Azkaban the incantation for the Banishing Charm is "Depulso".