It means that it includes every possible measure. So for example in research methods you want to make sure that your variable is mutually exhaustive. I can't have my variable as "political party" and only include democrats and republicans. There are people that are moderates or independents, therefore my survey would exclude these people--->which is being biased, and pretty much sucky research. So you have to make sure that you include everyone or that your variable is mutually exhaustive.
If the sum of events is sample space or a universal set then the events are known as mutually exhaustive. These events can be mutually exclusive and non-mutually exclusive.