Slow Rinse is usually an extension of the Brine Draw cycle. Once the entire brine volume has been drawn from the brine tank, the air check valve (floating ball) closes so that air is not drawn into the softener.
The Slow Rinse continues which pushes the brine through the resin whereby it is eventually rinsed from the resin to the drain along with the calcium and magnesium ions released during the cycle. The brine needs to have adequate contact time with the resin for the ion exchange to occur so the brine and slow rinse is done slowly.
There is usually a 1 to 4 ratio between the brine draw time vs the total slow rinse time. As it typically takes 15 minutes to draw the brine from the brine tank, the total Brine/Slow rinse cycle should then be set for 60 minutes.
While the Rapid Rinse cycle will rinse away any remaining brine residue, the main purpose is to settle and pack the resin, so that in-service water flow is forced to flow through the resin as opposed to flowing around the resin as would occur if the resin was loose.
The initial Backwash portion of the regen cycle, not only washes away any debris from the resin, but also loosens and redistributes the resin which permits the brine to easily flow between the resin beads, thereby having more complete contact with the resin.