A windmill is a discovered check you can play over and over. The rook gives check right next to the king, the king has one square to go to, and then the rook swings off the line so the bishop behind it gives check instead. Every swing costs Black a pawn or a piece, and Black never gets a move in.
The most famous one is a hundred years old.
Torre against Lasker, Moscow 1925
Carlos Torre had the white pieces against Emanuel Lasker, world champion for twenty-seven years. White’s rook sits on g3, the bishop on g5, and the queen on h5 is doing nothing very much. Torre played 25.Bf6, offering the queen.
6 
5 
2 e 
g Lasker took: 25…Qxh5. Then 26.Rxg7+ Kh8 (the rook on g7 is poison, the bishop on f6 guards it) 27.Rxf7+ Kg8 28.Rg7+ Kh8 29.Rxb7+ Kg8 30.Rg7+ Kh8 31.Rg5+ Kh7 32.Rxh5. Four turns of the wheel: the g7 pawn, the f7 pawn, the bishop on b7, and finally the queen back. Torre came out three pawns up and won.
Count Lasker’s moves in that sequence. Every single one was a king move, and every single one was forced.
Why the king is stuck on the wheel
Three things hold it together. The bishop on f6 attacks h8 through g7, so as soon as the rook leaves g7 the king is in check again. The king has exactly two squares, g8 and h8, because the h6 pawn and White’s rook take the rest. And the rook, standing next to the king on g7, cannot be captured, because the bishop defends it.
Take away any one of those and the machine stops. Give the black king a flight square on h7 and there is no windmill at all, which is one more reason to think about making luft before the position gets sharp.
What to look for in your own games
You will not find a windmill by hunting for windmills. You find it by noticing the ingredients: your rook and bishop pointing at the same corner, the enemy king with two squares, and a check available next to it. Then ask the greedy question. If I check here and he steps aside, what does my rook get on the way back?
That is the same question behind every discovered attack, and the windmill is just the version where you get to ask it four times in a row.