A categorical variable is a variable whose values are categories.
Examples: blood group is a categorical variable; its values are: A, B, AB or O. So too is construction type of a house; its values might be brick, concrete, timber, or steel.
Categories may have numerical labels, for example, for the variable postcode the category labels would be numbers like 3787, 5623, 2016, etc, but these labels have no numerical significance. For example, it makes no sense to use these numerical labels to calculate the average postcode in Australia..