The staircase has a nice maneuver if you keep on checking the king until it is mate. It is kind of like the 2 rook mate, but much more easier. It is kind of like a pattern. You'll see what I am talkig about in the following position.
Here white has two rooks and can easily checkmate the king, but there is a much easier way if you use the staircase trick 1.Ra3+ (1.Raf2 is a much faster way to checkmate the king, but 1.Ra3+ is a much easier way to checkmate the king). 1...Kf4 and here is how the mate follows:
After taking a look at this diagram you might see the pattern here. As the two rooks keep on checking the king until it's mate.
This information is from Jeremy Silman's Endgame course