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.

The importance of slip in an induction motor is, that the phenomenon SLIP makes the motor work. Slip is what makes the rotor experience a rate of change of magnetic flux due to the surface of the rotor running slower than the rotating field of the stator, which will induce a voltage in the rotor, which in turn will produce current in the short circuited bar windings on the rotor, which will create a magnetic field, which will react on the original rotating magnetic field set up by the stator to drag the rotor to achieve its rotation. If there is no slip there is no magnetic field set up in the rotor to react with the rotating magnetic field of the stator.

If in the rotor a permanent magnet is introduced then the slip is not necessary as the permanent magnet in the rotor will run in a synchronized manner with the rotation of the stator.