When a substrate competes with and inhibitor, what they are actually doing is competing by the active site of the enzyme. In terms of probabilities, when there is much more of one molecule of X than its competitor Y, it is more likely for any of the molecules of X to reach the active site of the enzyme than for any of the molecules of Y.
Then is one would like to reduce the effects of an inhibitor reversible bonded to an enzyme, one possibility is to increase the concentration of a substrate (which in turn means that there will be a higher relative number of its molecules in the media), increasing the probability to meet the active site of the enzyme and as a result displacing the inhibitor (assuming it not increased as well).
