A Dyck path is a staircase-like path that starts at the origin in a coordinate system and moves only up or right. It consists of steps that go up one unit or right one unit, and it never dips below the horizontal axis. These paths are often used in combinatorics and are related to various mathematical structures, such as Catalan numbers. Dyck paths can represent valid sequences of parentheses or lattice paths in a grid. They are useful in counting problems and have applications in computer science, particularly in algorithms and data structures. The study of Dyck paths helps in understanding combinatorial structures and graph theory.