The numbers may represent categories, or serve to distinguish groups. The numbers do not reflect differences in magnitude or quantity. Some examples may include identifying subjects' Gender, Ethnicity, Class, HairColor, and the like. You would not use an arithmetic Mean to describe the groups. You could describe predominance with groups using measures such as Mode, though.
Ordinal data identify subjects by position in a series.
These data reflect the order or ranking of elements in some kind of scale or arrangement. Numbers generally indicate rank order of observations. Some examples may include ranging subjects by height, or order of finish in a race, or relative academic standing in their class. A measure of Average, or Mean, would be meaningless with these data. You could describe Median tendencies of the data, however.