Most commonly, we wish to compare whether a certain dependent variable differs between independent groups of observations. For instance, you might wish to compare sales levels between:

The idea here is that the groups are independent, because an observation cannot be classified into more than one group. For instance, people can typically fall into only one gender (unless some very interesting biology is at play).

In addition to comparing independent groups, we can also compare data across related categories, that is, categories that are not independent groups but where the observations are related in some way as described below.

For instance, we may measure reactions to a brand before and after an advertising campaign. If we measure these reactions on the same people, this means that each person gives two pieces of data at two different times. The fact that each person gives data to each time period measurement makes the data related. Time period becomes the categorical differentiator, and the categories are related by virtue of this design.