The idea is simpler than the name suggests. You own a car. For whatever reason, on a particular day or for a particular stretch of time, you would rather not be the one driving it. A safe driver is the person who fills that gap: he comes to your address, gets into your car, and drives you wherever you are going.
That is the part people find useful. A taxi means leaving your car behind and coming back for it later. Renting means paperwork, a deposit and a vehicle you do not know. With a safe driver in Dubai, none of that changes hands. The child seat stays fitted, the parking permit stays on the windscreen, your sunglasses stay in the door pocket, and the car goes home with you at the end of the night.
The bookings vary enormously. Three hours on a Thursday evening, every weekday morning for the school run, or once after surgery and never again. What they share is that the car was never the problem — the driving was.