What is Contingent claim and replication?

A contingent claim is a payoff at $T$ that depends on the state: a vector $g\in\R^S$ in the one-period model, a random variable $g(S_T)$ or $g(S_t, t\le T)$ in general. A replicating portfolio for $g$ is a portfolio of traded assets whose payoff equals $g$ in every state: $D\theta = g$.