The answer to the riddle "What gets bigger the more you take away from it?" is "a hole." When a hole is dug, it grows larger as more dirt is removed. Thus, a hole gets bigger when more is taken away from it.
This riddle belongs to the category of "What am I?" riddles. These riddles are usually quite short. They sometimes involve wordplay but do not require the solver to puzzle out a scenario. "A hole" is the answer to another riddle as well: "It cannot be seen and weighs nothing, but when put into a barrel, it makes it lighter."