In a random walk one defines a mathematical entity called a walker, whose attributes completely define the state of the system in question.
The state of the system can refer to any physical quantities, from the vibrational state of a molecule specified by a set of quantum numbers, to the brands of coffee in your favourite supermarket.
The walker moves in an appropriate state space by a combination of deterministic and random displacements from its previous position.
This sequence of steps forms a chain.