There is an excellent article which explains Martingale on Wikipedia, but for anyone not wishing to study the mathematics in too great a detail, the concept is probably best explained simply by considering a flip of a coin.
There are two possible outcomes, heads or tails. Let's suppose you bet $1 that the coin will land heads up. If it does land heads up you win $1. If it lands tails up, then on the next flip you apply Martingale and bet $2. If it lands the right way, you win $2 but remember you just lost $1, so you really only win $1.
But what if it lands the wrong way? Then you simply bet $4 on the next flip. If it lands the right way you'll win $4 less the $3 you've already lost, leaving the net gain at $1. If it goes wrong, you'll be down $7 overall, so you'll bet $8 on the next flip to claw the loss back and still end up with a $1 profit.
At the end of a losing run, you'll always recoup your losses and win $1. How cool is that?
So what's the catch?
Well actually there are several catches.
The first mistake that people make is believing that what has happened in the past will statistically influence the future. Just because you've called the coin flip wrong 10 times in a row, the odds of getting the next flip right are still exactly 50:50. They're no higher nor are they any lower because of past performance.
The second mistake that people make is that they don't realise quite how quickly the money gets eaten up when you double up after every losing trade. When you are betting $1 on the flip, it doesn't sound like a lot of money and it isn't. But after 5 losing flips, the stakes will have increased to $32. And they will increase to $64 after the sixth losing flip. And so on ....
Just ask yourself for one moment .... Would you ordinarily bet $64 on a single flip of a coin where the odds of success are evens? It's my guess that most people would answer no to that question because they're considering it in the cold light of day and can think about a rational answer. But, in the heat of the moment after a few losses, people tend to act irrationally and end up regretting it later.
Of course, it goes even further than that, because if you do bet $64 and call it wrong, the stakes will increase further still. Eventually YOU WILL RUN OUT OF MONEY AND WON'T BE ABLE TO AFFORD TO TAKE THE NEXT BET.
When you apply Martingale to Forex the same situation applies, with the major difference that people don't appreciate quite how the leverage on their account makes them risk far more than they think. Whereas it's easy to withstand several successive losing coin flips, it's a lot more difficult to withstand the same number of successive losing Forex trades where Martingale is at work. Ironically, the players who tend to rely most on Martingale tend to be those players with the smallest accounts and the maximum leverage who can least afford the extra risks.
Martingale is clearly a game which is best suited to players with very deep pockets. I'm not saying that people shouldn't use Martingale, but I do believe it's very important to run proper tests beforehand to discover exactly what the worst case scenario really is likely to be. Hopefully some of the testing work that I publish to this site will be of use to all the "Martingalers" out there.