Markov property

A state $S_t$ is Markov if and only if $\mathbb{P}[S_{t+1}|S_t]=\mathbb{P}[S_{t+1}|S_1,\dots ,S_t]$. That is to say, a Markov state $S_t$ encodes the history (past states), because to compute $\mathbb{P}[S_{t+1}]$, only the current state is needed, not the entire history.