The Fibonacci is basically a sequence of numbers that wasn't originally intended for blackjack or even for gambling, but since its creation people have tried adapting it to games like blackjack and roulette.
Rather than giving you a history lesson, I shall dive straight into things, here is the Fibonacci sequence of numbers:
1 1 2 3 5 8 13 21 34 55 89
This sequence is basically determined by your previous two numbers. The basic rule of the Fibonacci is as follows: Your next number is always the total of the previous two combined.
So using the above as an example again, the last number is 89 because 55+34 is 89. Now as you can probably guess, you start out at the left hand side of the sequence of numbers and work your way down as you lose your bets.
In some ways it's similar to the Martingale because you're increasing your bets as you lose. The two strategies vary though because when you get one win with the Martingale, you instantly recover all your losses and you can start over.
With the Fibonacci the progression that you use isn't as steep as you can see and while this is a good thing when you're increasing your bets, it also means that one win alone isn't enough to recover all your losses.
What you need to do is go back two stages in the sequence of numbers after a win and forward one after a loss. You repeat this process until you're back at the start, at which point you will be in profit.
Let's go through a quick example now to make sure that this is clear. Let's say that you just bet 55 and won, you will now go back two stages in the sequence of numbers which means that your next bet needs to be 21.
If you win this you then go back down to 8. Another win will send you back down to 3 and so on. Just to summarize what I've just said, always go forward one number in the sequence after a loss and always back 2 after a win.
The upside to the Fibonacci is that it's safer to use than the Martingale because your bets stay smaller for longer. Another upside is that you only need to win around half as many as you lose for you to still end up with a profit.
The downside is the same problem that strikes all strategies of this kind, if you go on a bad losing run you will end up having to bet large amounts and it can be hard to recover.
Like any strategy that you use, always set yourself up with a profit target and a stop loss limit and stick to it for better or worse. Also use the Fibonacci in conjunction with the blackjack strategycards that we have which will give you the best odds of winning long term (although it's not guaranteed obviously).