Mattress stitch is a method of joining two pieces of stockinette (or reverse stockinette) invisibly. See Lucy Neatby's mattress stitch tutorial for a photo of just how invisible this is.
How to do it
Start with Lucy Neatby's mattress stitch tutorial, which tells you pretty much everything you need to know.
Mattress stitch does rely on any increases or decreases being at least two stitches in from the sides of the pieces. It also hides one stitch at each edge, as these are drawn to the wrong side to form the seam, so you need to be aware of this if doing fancy colourwork.
This stitch is rougher than many on the yarn used to do the joining, as it's pulled through the fabric so many times, so it's best to use short lengths rather than one long one.
Rebecca Online's tips section suggests a variation on Lucy's basic technique that's useful for joining striped panels. They begin by picking up just one horizontal bar to get the rows lined up, and then pick up two from the other panel, two from the first, and so on.