In an efficient market, a discounted price is close to a martingale: the best forecast of tomorrow is today. Note that this is weaker than a random-walk, because a martingale allows the size of moves to be predictable even when the direction is not. Volatility can be forecastable while returns are not, which is exactly what markets look like.
This distinction is the foundation of volatility trading. You cannot reliably say where a market will be, but you can often say how far it will travel, and that is a tradeable quantity through options or volatility-targeting.
Do not confuse this with the martingale betting system, doubling after every loss. That is an unrelated and reliably fatal money-management scheme, since its bankroll requirement grows exponentially while its edge stays negative.
Related: random-walk, efficient-market-hypothesis, markov-property, risk-of-ruin