The Martingale system is the oldest betting system. It's risky and virtually useless in todays casinos. Spread of Martingale systems was one of the original reasons the casinos decided to implement table limits as the casinos seriously feared for their well being back in the old good days. Betting limits make Martingale systems effectively pointless.
Basically, Martingale system prescribes you to double your bet every time you lose so that your next win will cover all the losses from previous games. Originally intended for games in the long run, this strategy is stripped of its glory today because the table limits prevent using it for any prolonged period of time.
There are very few situations where the Martingale system can come in handy. We don't recommend practicing it in real money games unless you know exactly what are you doing. The Martingale system is less stable than, say, Level 2 Progressive Betting on shorter game periods and is useless for longer game periods.
The Martingale system has an opposite, the Paroli system and its minor modifications.