Most faucets work with a rubber or composition washer that closes onto a metal washer seat. Over time, the washer will harden and crack or simply gets worn down. This causes the faucet to leak. You can close the faucet tighter to stop the drip, but this will only be a temporary fix. In fact, you’re just increasing the internal damage to the washer and faucet and the problem is only going to get worse. Usually when the faucet drips, the problem has a relatively simple solution: the washers or other internal mechanisms need to be rebuilt or replaced. You can do this yourself or contact a professional plumber who can fix this easily and inexpensively.