Technically, a "Soft Start" (as it relates to AC electric motors) is any device that will reduce the toque delivered to the power train. Mechanically, this can be a clutch, fluid drive, magnetic coupling, shot coupling or any one of a variety of devices that allow the motor to start-up Across-the-Line (X-Line or D.O.L.) while slowly applying the shaft torque to the load to avoid "torque shock". Electrically it can be any system that reduces the torque by virtue of reduced voltage, or a change in the motor connection.
Changing the motor connection means altering the way the windings are configured so that a reduced torque is put out from the motor, even though the voltage is normal. Case in point would be a Y-Delta (Star-Delta) starting method, or a Part Winding start. Both of those methods require a motor that has been designed to be capable of starting that way, and as such they are not universally available.
Changing the motor terminal voltage reduces the torque because the motor output torque (at a fixed frequency) varies by the square of the applied voltage. So if 50% voltage is applied to a motor, it will produce 25% of it's available torque at that point. If it is a Design B motor, the Locked Rotor Torque at Start-up is typically 160% of Full Load Torque, so starting at 50% Voltage will reduce that to 40% of FLT, limiting the torque shock to the load.
Reduced Voltage starting can be accomplished in several ways as well. A common method is to use an Autotransformer that drops the motor voltage during starting, then is switched out so that the motor gets full voltage when running. This method is called Reduced Voltage Auto Transformer (RVAT) starting. Similar to this are Reactor and Primary Resistor starters which drop the voltage through those devices as well. All of the above technologies can be and often are referred to as "soft start" devices, but more recently this terminology has come to usually mean one specific type, the Solid State Reduced Voltage starter.
The SSRV starter uses high speed switching devices called SCRs (Silicon Controlled Rectifiers) to switch on for only a portion of each half of the sine-wave line power. By doing so, the RMS (roughly average) voltage getting to the motor is reduced proportionately by the amount of time the switch is delayed. So if the SCR is not allowed to begin conducting (know as being "gated") until the sine-wave is already 1/2 over with, the output RMS voltage will be 1/2 of the line voltage. By moving the "gate" point further back in the sine-wave, the RMS voltage is increased until the SCR is being gated at the Zero-cross point and the motor is getting full line voltage. The speed at which the SCR gating is backed up is called the Ramp Time, and can typically be anywhere from a fraction of a second to 60 seconds. Although longer times are technically possible, most AC motor applications will not allow this because the increased current caused by the reduced voltage will begin to exceed the thermal safety limits of the motor itself, particularly the Rotor. In addition, the ramp time can be overridden by a Current Limit setting, which determines the motor current through feedback sensors and stops the gate advancement in order to maintain a particular current setting. This feature is useful when the power system has limited delivery capabilities, such as weak utility lines or portable generators.
Finally, once the motor is at full voltage the SCR firing becomes unnecessary and it is often beneficial to use a Bypass Contactr to shunt power around the SCRs. SCRs are not perfect conductors, and will reject approx. 1.5 watts of heat per running load amp per phase. So on a 3 phase 100A motor, the SCRs will be rejecting 450W of heat into the enclosure continuously. A Bypass Contactor is a good way of avoiding that heat buildup without introducing dust, moisture or other contaminants into the enclosure.