My first guess is that it’s a condensate drain line for your air conditioner. Second guess is a dehumidifier drain. Third guess (thanks to @crip659) is a broken pressure valve on the hot water heater.
- Pressure release valves, in my experience, are easy to open, but not so easy to get them to close again. They sometimes seem like single-use valves! You may need to replace this valve. To see if this is the problem, turn off the water and the water heater. This can leak even if the water is shut off, as the heating water can expand and overflow even if there’s no mains water pressure.
If that’s not it, shut off the main water to the house, and see if it keeps dripping.
- If it does, the water is coming from the air, not the pipes. Shut off each circuit breaker, check if the water is still leaking. That should narrow it down to one appliance.
- If it stops, it’s a plumbing leak. Try to follow the pipe to figure out where it’s connected on the other end.