One of the fundamentals of singing has to do with the muscles and how we get them to move.
Of course, restoring lost movement is a primary goal of vocal exercises. For example, staccato exercises are valuable for instituting the closing and opening of the cords, especially if they have been separated and “locked out.”
The Sliding Exercise, on the other hand, has a different purpose.
These exercises are valuable for engaging the stretcher muscle system (crico-thyroid or “falsetto” muscle). If the closer is closing and able to hold, then the stretcher muscle can start to pull opposite to the hold of the arytenoids; stretching and thinning the cords.
The singer will feel a slide up and a slide down. The sliding maybe only a short distance at first (interval of a 2nd or 3rd). This is like stretching a rubber band slowly, holding both ends, and letting it go back to the original shape.
The slide is both for development and coordination; building muscle and at the same time teaching the muscles how to be in a balanced equilibrium. This will, at a point down the road, be the makings of a fine legato or smooth vocal line when singing.
A word of concern: sliding has a purpose and should not be treated as a warmup exercise done without thought. This exercise could do more harm than good by dragging improper adjustments up and down. Therefore, when one slides, one should feel and think much so that one is allowing the proper adjustments all the time.