Constructible sets are one of the central notions in descriptive set theory.
In set theory, a (Gödel) constructible set is any set in a constructible universe, see there.
One can generalize to constructible elements in more general Boolean lattices.
In general topology, given a topological space $(X,\tau)$, a constructible subset of $X$, sometimes (when $(X,\tau)$ is fixed) often simply referred as a constructible set, is an element of the smallest Boolean algebra of sets containing the topology $\tau$; the constructible sets are precisely the finite unions of locally closed sets.
In the case of theory ACF of algebraically closed fields, for every model $K$, the constructible sets in the affine space $K^n$ are precisely the definable sets for the language of fields.