vA standard 3-pole wire wound servo motor uses a steel core with wires wound around the core, this core is then surrounded by permanent magnets.
As you can imagine, the core and all that wire weighs a fair bit. When voltage is applied to turn the motor, it has to first overcome this weight to get things turning – it is slow to accelerate. Once up to speed, it also continues to turn for a while when the voltage is removed – it is slow to decelerate.
In a Coreless design, the heavy steel core is eliminated by using a wire mesh that spins around the outside of the magnets. This design is much lighter resulting in quicker acceleration and deceleration. The result is smoother operation, more available torque, and faster response time.