In the case of a tandem dual-thrust motor, the fuel nearest to the rocket nozzle burns fast, and the fuel further into the motor's body burns slower.
This gives the rocket higher thrust initially, accelerating it rapidly to high speed.
The advantage of dual-thrust motors is that if the fuel were entirely the fast-burning type, the rocket would accelerate to a higher speed initially but because air resistance increases quadratically with speed, the rocket would slow very rapidly.
Dual-thrust motors are most prevalent in rockets which are atmosphere-bound since they have to deal with air resistance over most of their flight.
It is similar in concept to multistage rockets, but much simpler to design and build since there is no requirement to detach stages, have separate components, etc.