It's basically working things out from a mathematical point of view. If you haven't got the players to play good football you usually play percentage football whether you realise it or not.
It's basically saying 'if we get the ball here x amount of times there's a good chance this will happen'. For example, if you get the ball to your wingers they might beat the full back 50% of the time, and get a good cross in 50% of the time they do that. So if you move the ball wide there's a 25% chance there'll be a good ball into the box. 50% of the time your forward will get his head on it, and he'll score 50% of those headers. This is all very simplified, but basically some people would figure out from all this that if your wingers get the ball with a one on one run against a full back you'll score 6.25% of the time. Do this 20 times over the course of 90 minutes and you'll score at least once.
And if you play a long ball to a forward who has another man with him up there, there might be a 50% chance he'll win a flick on. Taking into account that one defender has been dragged out to win a header, the other forward has a 50% chance of winning the loose ball. Therefore a 25% chance you'll have the ball in their half.
There's also something called the POMO (Position of Maximal Opportunity), which is basically the opposition box. Stats say if you get the ball into the POMO enough times you're going to create chances from a certain percentage of them, whether that's by winning headers, defenders making mistakes etc.
In short it's what Sam Allardyce does, but it's different to just a long ball game, which is what most people think of when they hear 'percentage football'. All coaches use it in a way, just not as strictly.