What is the importance of slip in a 3-phase induction motor?

The rate at which the flux cuts the rotor conductors is directly proportional to the difference between the speed of rotating field (N s) and that of the rotor (N). If the rotor speed were to become equal to the speed of the rotating field, there would be no generated e.m.f. (and hence current) in the rotor conductors. Consequently, there would be no motor action. Thus it is the slip of the rotor (Ns – N r.p.m.) which causes e.m.f.s to be generated and currents to flow in the rotor conductors. This is precisely the principle of operation of 3-phase induction motor.

Slip creates a relative speed between the RMF and rotor. That keeps a torque continuously acting on it when the motor is running.
So what would happen if slip becomes zero?
Bcoz there will be no relative speed between RMF and rotor, and which will stop inducing rotor current. This will stop the production of rotor flux, thus no torque will be generated. As a result, the rotor will cease to rotate in the absence of running torque.
The importance of slip in the induction motor can be discussed below based on the values of a slip because the motor behavior depends mainly on the slip’s value.