What does 'random effect' mean?

What is it about?

In general in statistics, and in particular in meta-analysis, the term 'random effect' is used in two different ways. In meta-analysis it is used on the one hand to describe random variation from trial to trial of health outcomes, irrespective of treatment given and on the other to describe random variation from trial to trial of the difference (compared to control) that treatment makes to health. These can be described as random main & random interactive effects, respectively.

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Why is it important?

Modeling the main effects of trials as random permits direct comparison of results from one trial to another and tends to decrease standard errors. Modelling treatment-by-interaction as random allows the true effect of treatment to vary randomly from trial to trial and leads to larger estimated standard errors.