One of my toilets had the runs. It would randomly start flowing for a minute or so, then stop with a loud thunk. Unfortunately, I only noticed it when I was in bed (with my head on the other side of the wall from the toilet), so I couldn't be arsed to do anything about it at the time. Then I'd forget during the day. Eventually I decided to deal with it while waiting for some Doctor Who episodes to finish downloading. I mean blind kids to finish being read to.
This page was helpful in figuring out what the bits do. I'll just supplement the Internet's existing excellent information with my own special incompetent perspective.
I found the flushing mechanism rather clever. When you push the handle, it lifts a flap which otherwise plugs the bottom of the tank. Water flows from the tank to the bowl, then down the drain, flushing any let's say "goldfish" down with it. The force of flowing water holds the flap open until the water mostly drains; if you need more flushage you can hold the handle down to let the tank drain completely. Meanwhile, as the water drops, a float drops; the float is connected to a valve. The dropping float opens the valve and lets new water flow into the tank, but not quickly enough to prevent the tank from draining. More water also flows into the bowl. When the water level in the tank drops enough, the flap at the bottom closes, plugging the tank. The new water flowing in begins to fill the tank and bowl. As the water level rises, it lifts the float, which eventually closes the valve and stops all water flow.
Next: diagnosis and repair.