Refers to data generated from a distribution that has a countable sample space. The discrete data tag may encompass categorical data, whether nominal (e.g. the distribution of race in a sample of individuals) or ordinal (e.g. socio-economic status), or an actual discrete random variate, such as a set of event counts (e.g. the number of errors on a page of text). Discrete data need not necessarily be integer, however.

From Mood et al. (page 57, 1974):

"A random variable $X$ will be defined to be discrete if the range of $X$ is countable. If a random variable $X$ is discrete, then its corresponding cumulative distribution function $F_X( . )$ will be defined to be discrete."

Mood, A. M., Graybill, F. A., & Boes, D. C. (1974). Introduction to theory of statistics. (B. C. Harrinson & M. Eichberg, Eds.) (3rd ed., p. 564). McGraw-Hill, Inc.