A Markov property refers to any of a certain class of independence properties of Random variables defined on the nodes of a Network.
Pairwise Markov property: Any two non-adjacent variables are conditionally independent given all other variables
Local Markov property: A variable is conditionally independent of all other variables given its neighbors (video).
Global Markov property: Any two subsets of variables are conditionally independent given a separating subset
See here, and Markov network
Stochastic processes that satisfy the Markov property are known as Markov process