A silent toilet leak is a common problem that occurs when the fill valve of a toilet does not shut off completely when the water rises in the tank. It may appear to shut off and go quiet after the tank fills up, but a tiny bit of water is leaking by unnoticed into the tank.
The water level inside the tank will slowly rise until it gets to the height of the overflow tube. It stops at that level as the excess water slowly trickles down into the bowl and down the drain.
Unlike a leaking flapper (which will often result in the toilet audibly kicking on from time to time when no one is using it), a fill valve that is malfunctioning in this way has extremely subtle symptoms and can go unnoticed over a longer period of time.