The step-down is a lateral step-up variation that begins at the top of the motion rather than the bottom.
Stand with one foot on a box or bench and the other foot off to its side. Under control, squat until the toe of the free foot gently touches the floor, then without using it to push off at all, stand again. Hold onto a rack or similar to assist as needed.
The step-down provides unilateral leg strength for better balance and to reduce weaknesses that limit bilateral leg strength, improves hip stability, and stresses knee extension in the most mechanically difficult range. The choice of the step-down over the step-up is typically to allow more control of the entire range of motion (i.e. not helping the concentric start with the other leg), and being better able to control assistance—this makes it a good exercise for rehab and prehab, but also as a way to build initial strength for more challenging unilateral exercises.
The step-down can be performed with added weight held any way possible with any step-up variation (1 or 2 dumbbells or kettlebells at arms’ length or on the shoulders, a barbell on the back or clean rack positions, 1 or 2 weights overhead, etc.). The position can also be changed to a traditional step-up, but this requires more forward leaning for balance so changes the effect considerably. The trunk can be kept more upright (as much as completely vertically) by holding onto a rack or similar at the side. Finally, very slow eccentrics can be used as a prehab or rehab method for the knees, or as a way to develop the initial strength to perform the exercise.