The flapper needs to make a seal around the outlet of the tank to ensure no water gets out.
If the flapper is really old and corroded, then @saint‘s suggestion to replace it makes sense.
Else, it might just be that some little speck of trash has gotten in the way of a good seal, or perhaps the chain has fallen off the bar from the handle, or some other such easy-to-remedy problem. In that case, @janbb‘s suggestion makes sense.
There’s another possibility in that the fillup cutoff mechanism might be allowing the water level to get too high and your tank is spilling excess water down the overflow tube (which prevents it from flooding your bathroom).
Remove the cover from the tank in the back of the toilet and set it aside. Then jiggle the handle and watch what happens. Finally, push the handle all the way and see how it all goes.
Home Depot offers a pretty helpful little video, too.