The problem is yout toilet flapper. It will look something like this.
You can find a new one at most hardware stores or at a stoe similar to a Lowe's or Home Depot. Changing them is very easy, usually they are held by two ears on either side of the standpipe. Just remove the old one, hook on the new one and adjust the chain to the lever so that it flushes properly.
These are made of soft plastic or rubber and are affected by stuff in the water. Chlorine especially is hard on them and makes them hard and brittle, causing them not to seal right.
Sometimes dirt will accumulate on the bottom and wiping the bottom off will fix the problem, but it is usually a temporary fix.