The future depends only on the present and not on the past.
Let $X_0, X_1, \ldots, X_t$ be a Markov Chain and write $P(X_t = x_t | X_{t-1} = x_{t-1})$ as $P(x_t | x_{t-1})$ for instance. Then
$$ P(x_t | x_{t-1}, x_{t-2}, \ldots, x_0) = P(x_t | x_{t-1}) $$ The next step of the Markov chain only depends on the current state and not on how we got to that state.
Markov Chains