It's a variable that deals with various labels, rather than the usual type of numeric variable you may be used to.
One example of a categorical variable is color. You could have red, green, blue, yellow, and orange as the five choices for your categorical variable. Each color is a label or category.
This is an example of a qualitative variable. We don't have any numeric data attached to color. They're simply names or labels. In contrast, a quantitative variable is something like a person's height since a number is attached here (more specifically its a continuous quantitative variable).