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 . 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 $k+1$th round. See the Wikipedia page for examples of martingales. The course notes is fabulous. I am following it on and off!