A sequence of random variables $$X_0, X_1, \dots$$ with finite means such that the conditional expectation of $$X_{n+1}$$ given $$X_0, X_1, X_2, \dots, X_n$$ is equal to $$X_n$$, i.e., $$\mathbb{E}[X_{n+1}\mid X_0, X_1, \dots, X_n] = X_n.$$
A one-dimensional random walk with steps equally likely in either direction $$(p=q=\frac12)$$ is an example of a martingale.