A Hilbert scheme is a mathematical construct that parameterizes families of subschemes of a given algebraic variety. It allows mathematicians to study the ways in which smaller geometric objects, like points or curves, can fit into a larger space. These schemes are particularly useful in algebraic geometry, as they provide a way to understand the structure and properties of varieties by examining their substructures. The study of Hilbert schemes has connections to various areas, including moduli spaces and intersection theory, making them a vital tool in modern mathematics.