A random effect is one that might vary if you repeated the same study; for example, the skill level of participants, or weather on the day of an experiment. Random effects need to be treated as an additional source of noise. Contrast with a fixed effect.
Also used in hcistats2e: Chap. 1: page 9; Chap. 5: page 63; Chap. 7: page 76; Chap. 14: page 174