Refers to data generated from a distribution that has a countable sample space. Discrete data may be nominal (e.g. the distribution of race in a sample of individuals) or ordinal (e.g. the number of errors on a page of text).
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."