A nice intuitive to way to explain what a Martingale is found here (Venkat’s Computational Probability course notes). Perhaps it was known already to many. To a layman, this is the best way to introduce Martingale, first up!

A sequence X_{1}^{n} =X_1,X_2,X_3,\ldots,X_n  is called a martingale if  \mathbb{E}\left[X_{k+1}|X_{k} \right]=X_{k}, for all 1< k <n. An intuitive way of thinking about martingales (and indeed the origins of martingales) is to imagine X_k as your total profit after the k th round of a gambling game. Then the martingale condition states that knowing your winnings in the first k games should not bias your winnings in the k+1th round. See the Wikipedia page for examples of martingales. The course notes is fabulous. I am following it on and off!