A reversible inhibitor is one that, once removed, allows the enzyme it was inhibiting to begin working again. It has no permanent effects on the enzyme - it does not change the shape of the active site, for example. Reversible Inhibition may be Competitive, Non-Competitive or Uncompetitive.
A competitive inhibitor directly competes with the substrate in a reaction. It will be a very similar molecule to the substrate - similar enough that it fits into the active site - but once inside the active site it will not be affected in any way by the enzyme. The inhibitor will probably have a higher affinity for the enzyme than the substrate does - however, a competitive inhibitor can be overcome simply by adding more substrate. With enough substrate, the chance of a collision between the substrate and an enzyme is much higher than the chance of a collision between an enzyme and the inhibitor, causing the effect of the inhibitor molecule to be overcome.
The inhibitory molecule in this case does not bind to the active site, but to another site known as the Allosteric site. The substrate may still bind to the active site of the enzyme, but the enzyme will be unable to affect the substrate, and thus no product is produced. As this form of inhibition cannot be overcome by increasing concentration, cells must have other methods to overcome this, by removing the inhbior and allowing the enzyme to resume function.
Only takes place in multi-substrate reactions.