Multiple comparisons are used in the same context as analysis of variance (ANOVA) - to check whether there are differences in population means among more than two populations. In contrast to ANOVA, which simply tests the null hypothesis that all means are equal, multiple comparisons procedures help you determine where the differences among the means occur.
In a broader sense, multiple comparison procedures can be applied to testing for differences in population parameters other than the mean. The logic remains much the same.
Multiple comparison procedures rest on application of the same test to each pair of populations. Of course, the more tests (comparisons) you do, the greater the chance that you will see an apparently extreme difference just by chance. Hence, a main problem here is
1. Establishing and maintaining an appropriate probability of family-wise type I error
2. Based on the family-wise type I error, calculating the probability of comparison-wise type I errors
For some approaches to multiple comparison, see Bonferroni adjustment, Tukey´s HSD test.