Coins in medieval Europe were based on gold or silver. The purpose of clipping was to remove slivers of this material from the edge of the coin. Do this enough times and you have enough material that it can be melted down into either bullion or new coins.

Medieval governments tended to take this debasement of currency fairly seriously, with a number making clipping and counterfeiting a capital offence (eg 15th C England). [Edit: Worth noting, as an aside, that the problem persisted right up to the end of the 17th C when modern minting techniques (particularly milled edges) finally stamped out the process. In England, everyone's favourite slightly odd physicist, Isaac Newton, was at the forefront of efforts to end the problem.]