It sounds like a leaking flapper inside a toilet tank. The tank water level leaks down so any water pressure change (turning a faucet ON) allows the fill valve to bring tank level back to normal. If allow to sit unused for a long time(overnight), the water level gets low enough by itself to turn the refill valve ON. Replace the flapper and ballcock (fill valve). Learn more here: http://www.toiletology.com/leaking.shtml
