“A random-effects model provides a result that may be viewed as an ‘average intervention effect,’ where this average is explicitly defined according to an assumed distribution of effects across studies. Instead of assuming that the intervention effects are the same, we assume that they follow (usually) a normal distribution. The assumption implies that the observed differences among study results are due to a combination of the play of chance and some genuine variation in the intervention effects.
“The random-effects method and the fixed-effect method will give identical results when there is no heterogeneity among the studies.”
Definition taken from the Cochrane handbook (10.10.4.1