In a complex biochemical system, it is necessary to control the rate of biochemical reactions. For example, if we have a meal with lots of carbohydrate, we need to control the rate at which that is converted to glucose so that enough is present to provide the energy for our activities, but not so much as to put us into a diabetic condition. One of the ways in which this is done is by enzyme inhibition. The most direct way is to provide a molecule which fits into the enzyme's active site but doesn't react with anything there. There's still just as much enzyme around, so the maximum rate isn't changed, but some of the enzyme molecules are occupied by inhibitor.
Some enzymes show another pattern when an inhibitor is added.
In these cases, the enzyme's maximum rate is decreased. It is as if the enzyme has become a less efficient catalyst. When this happens, the folding of the enzyme changes a little bit, and the active site is distorted in a way which makes it a less effective catalyst. While the number of enzyme molecules hasn't changed, each of them is less efficient as a catalyst. In an experiment like the one we discussed above, we would see that an inhibitor which works this way would produce a decrease in the maximum rate.