The active site of an enzyme is the place on the enzyme molecule where the substrate (the substance which participates in the reaction catalysed by the enzyme) normally binds. 

Competitive inhibitors slow down enzyme action by acting at the active site - they bind to the active site of the enzyme molecule to prevent the substrate binding, so that that the reaction cannot be catalysed by the enzyme. The name "competitive" comes from the idea that the inhibitor "competes" to bind to the active site with the substrate. You can overcome the effect of a competitive inhibitor by simply adding more substrate so that the "competition" tips in favour of the substrate instead of the inhibitor.

Non-competitive inhibitors act at a site other than the active site on the enzyme molecule, so they don't actually "compete" with the substrate to bind to the active site. They act by changing the shape of an enzyme molecule once they bind to it, which also changes the shape of the active site. So, the substrate cannot bind to the active site anymore. You cannot overcome the effect of a non-competitive inhibitor by adding more substrate - the shape of the enzyme is changed permanently and the substrate will not bind to the active site no matter how much is present.