Essentially it means increasing or decreasing resolution by increments or steps, until the desired resolution is achieved. There have been wild postulations that involving using even step increments if you want to get to an even numbered final resolution, etc.
This method of increasing resolution may have some basis in fact with other programs, but not with photoshop.
In principle, increasing the resolution of an image is "fudging" by putting in artificial pixels, based on the surrounding pixels. Using a stair interpolation method you only increase the error of those pixels, by magnifying the error in the first round of upsizing.
Some have claimed visual improvements using stair interpolation, but I've never seen it, and I know of no one whom I respect in this forum that has reported success with this method. In other words, by most accounts, it's hogwash.
Peace,
Tony