To add to what DickDV has stated, the following is an excerpt from "Alternating Current Fundamentals" by John R. Duff and Milton Kaufman, chapter 16 (Three-phase induction motors)
Synchronous Speed and Percent Slip
The field set up by the stator winding cuts the copper bars of the rotor. Voltages induced in the squirrel-cage winding set up currents in the rotor bars. As a result, a field is created on the rotor core. The attraction between the stator field and the rotor field causes the rotor to follow the stator field. The rotor always turns at a speed which is slightly less than that of the stator field (less than synchronous speed). In this way, the stator field cuts the rotor bars and induces the necessary rotor voltages and currents to create a rotor field.
If the rotor is turned at the same speed as the stator field, there will be no relative motion between the rotor bars and the stator field. This means that no torque can be produced. A torque is produced only when the rotor turns at a speed which is less than synchronous speed.
As a mechanical load is applied to the motor shaft, the rotor speed will decrease. The stator field turns at a constant synchronous speed and cuts the rotor bars at a faster rate per second. The voltages and currents induced in the rotor bars increase accordingly, causing a greater induced rotor voltage. The resulting increase in the rotor current causes a larger torque at a slightly lower speed.
The squirrel-cage winding was described as consisting of heavy copper bars welded to two end rings. The impedance of this winding is relatively low. Therefore, a slight decrease in the speed causes a large increase in the currents in the rotor bars. Since the rotor circuit of a squirrel-cage induction motor has a low impedance, the speed regulation of this motor is very good.
Starting Characteristics
At the instant the motor is started, the rotor is not turning and there is 100% slip. The rotor frequency at this moment is equal to the stator frequency.
As the speed of the motor increases, the percent slip and the frequency of the rotor decrease. The decrease in the rotor frequency causes the inductive reactance and the impedance of the rotor to decrease. Thus, the phase angle between the stator and rotor fluxes is reduced. The torque then increases to its maximum value at about 20 percent slip. As the rotor continues to accelerate, the torque decreases until it reaches the value required to turn the mechanical load applied to the motor shaft. The slip at this point is between 2 and 5 percent.
Starting Current
At startup the stator field cuts the rotor bars at a faster rate than when the rotor is turning. The large voltage induced in the rotor causes a large rotor current. As a result, the stator current will also be high at startup. The squirrel-cage induction motor resembles a static transformer during this brief instant. That is, the stator may be viewed as the primary or input winding, and the squirrel-cage rotor winding as the secondary winding.
Most three-phase, squirrel-cage induction motors are started with the rated line voltage applied directly to the motor terminals. This means that the starting surge of current reaches a value as high as three to five times the full load current rating of the motor.