The normal tendency for people when facing off on the mat is to go as hard as they can, as fast as they can. BJJ can be practiced safely going full contact, so most people just want to go go go.
The experienced practitioner knows that this hard sparring has its place. However, there is another kind of beneficial type of rolling that teaches balance, technique, and position.
Flow rolling is when the two practitioners move relatively slowly, they focus on their technique rather than trying to smash one another. The catch is that when flow rolling you want to move smoothly, and try to execute your techniques just as you would if you were going full speed.
When you are rolling full speed, sometimes sweeps, position changes, or submissions happen so fast that you don't really know why or how they happened. When flow rolling you can see why you get swept in a particular position because you have time to feel your balance is off. When you are flow rolling you realize that when you are transitioning from side control to north-south, people are escaping because your hips are too high. When you flow roll you realize that you are getting armbared from mount because you are falling in to the opponent's trap by moving in to the armbar rather than knocking his balance off and doing a proper escape.
One of the primary reasons you should incorporate flow rolling in to your BJJ training regime is so that you can learn how movements work together. When you learn how movements work together you start to build a series of movements based on what your opponent does. What does this do for you? Well, if you have spent anytime talking and discussing BJJ, you have learned that the "good" practitioners are "two or three" moves ahead of their opponent. Well... how do they do this? Are they clairvoyant? Can they read my mind to know what I am going to do to be two moves ahead of me? No, but they know how moves work together and how the moves of their opponent can affect their own movements.
For instance, if my opponent is in my guard and he lifts his body up off of his heels, I can underhook my left arm underneath his right leg. From here I think ahead to my next two movements. I can pull on his left arm while lifting up on his right leg in a classic sweep.
As I complete this sweep, my choices branch. If the guy pulls his arm tight, I complete the sweep and to to mount, just as Joe Moreira demonstrated. However if the guy leaves his arm out, I don't pull my leg back, rather I use it to stop my movement, then swing it over my opponents head and I take the armbar. João shows this technique:
I know that these techniques dovetail in to one another. So, I can go from sweep to armbar before my opponent knows what is going on. What if the opponent knows the sweep, and defends by sitting back on his heels after I underhook his leg? With my left arm under his right leg I grab is right sleeve. I then bring my left leg up and around, scooting my hips out to the left. My opponent is caught in an omoplata.
Was I reading is mind? No, I knew that there were only a few different ways my opponent could get out of the situation, and I had the counters to those escapes in mind as I executed my game.
Moving at full speed, if I am not intimately familiar with these techniques and movements, I may not have time to put them all in my head. That leaves time for my opponent to complete his escape. When I am flow rolling, I have time to think about and put in to practice all of these movements. So that I can be come intimately familiar with them. The next time I roll full speed, the movements come to me as if I am reading my opponents mind.