A distributive lattice is an algebraic structure in which the operations of meet and join distribute over each other, meaning for any three elements a, b, and c, the equation a ∧ (b ∨ c) = (a ∧ b) ∨ (a ∧ c) and its dual hold true. This property ensures that distributive lattices can be represented using a subset of set theory, making them fundamental in areas like logic, topology, and computer science.