Problem with the water inlet valve ... hot or cold side, whichever. Could be a bit of debris is obstructing the diaphram from seating fully closed. Or the valve has just gone bad due to an internal problem with the diaphram, plunger, or spring. You can identify which side of the valve by turning off the cold supply faucet to see if the dripping stops. If not, then turn off the hot supply faucet. Valves years past could be disassembled to clear debris or even replace internal parts but nowadays they're usually sealed and can't be disassembled, must replace. It's not a large repair. Sometimes debris will loosen and flush through by tapping on the solenoid while it's on ... but sometimes not. Safest recourse is replace the valve assembly. The drip can get worse over time.

Ok, thanks very much for the helpful reply.