Parameters associated with the particular levels of a covariate are sometimes called the “effects” of the levels. If the levels that are observed represent a random sample from the set of all possible levels we call these effects "random".

Parameters associated with the particular levels of a covariate are sometimes called the “effects” of the levels. If the levels that are observed represent a random sample from the set of all possible levels we call these effects "random."

Reference:

Bates (forthcoming). lme4: Mixed-effects modeling with R.