How does inhibition of an enzyme-catalyzed reaction by a competitive inhibitor differ from inhibition by a noncompetitive inhibitor?

A competitive inhibitor is "competitive" because it binds to the same active site as the enzyme's natural substrate - the inhibitor competes with the substrate to occupy the active site. This is why if you add more substrate, it can overcome the inhibition because the substrate outcompetes the inhibitor. If you have green circles and blue circles both competing to occupy a round hole, the more circles of one colour you have, the more likely that colour will be to occupy the hole.

A noncompetitive inhibitor usually binds to a part of the enzyme other than the active site. The act of it binding to this other part can induce a shape change of the active site such that it will no longer be able to bind to its natural substrate. If you have a circular substrate for a round hole, but then the shape of the hole is changed to a triangle when the inhibitor binds, the circular substrate won't be able to interact with the enzyme no matter how much of it you have.