The meet of two elements a and b in a partial order is their greatest lower bound: the largest element c such that c ≤ a and c ≤ b.
Formally, a ∧ b = c requires: (1) c ≤ a and c ≤ b (c is a lower bound), and (2) for any d with d ≤ a and d ≤ b, d ≤ c (c is the greatest such). The meet may not exist in an arbitrary poset; when it exists for every pair, the poset is a meet-semilattice.
In a lattice, every pair has both a meet and a join. In a complete Heyting algebra, meets exist for arbitrary collections, not just pairs.
Meet corresponds to conjunction (∧, “and”) in the internal logic: a ∧ b represents the strongest claim that is entailed by both a and b individually. In Set, the meet of two subsets is their intersection. In a topology, the meet of two open sets is their intersection (which is open by the finite intersection axiom).
The Heyting implication is defined through meet by the residuation law: c ≤ (a → b) if and only if c ∧ a ≤ b. This makes meet left adjoint to implication — the two operations constrain each other through the adjunction.