A mixed effects model handles data that comes in groups (customers within markets, students within schools, repeated measures within patients) by mixing two kinds of coefficient: fixed effects, ordinary shared parameters, and random effects, group-specific offsets treated as draws from a common distribution whose variance the model estimates. The same object is called a multilevel or hierarchical model in other literatures.
The payoff is partial pooling: each group’s estimate is shrunk toward the overall mean by an amount calibrated to its sample size, which stabilizes small groups without distorting large ones, and standard errors stay honest in the presence of within-group correlation that ordinary regression would ignore.
