A small drip will get worse over time and eventually add up on your water bill. This can also begin to stain the sink if it is not taken care of fast enough.
If you suspect the faucet may be dripping you can use a paper towel or small container to test it out. Dry the sink up after using the faucet and place a paper towel under the spout and check back later to see if it wet. Also, a cup or bowl would work if you can get it in the right position and let it sit a little longer.
If the faucet leaks at the spout you might need to change the washers on the faucet or replace the faucet cartridge to repair the leak.