A soft start utilizes SCR's to provide variable voltage (at fixed frequency) to a motor during starting. The voltage is ramped up to full voltage over a time period that is usually user variable. More sophisticated soft starts use a closed loop current ramp instead of a fixed time ramp, meaning that the drive would be set to limit starting current to motor FLA (for example) and would accelerate as fast as possible at that current. Most modern soft starters use a bypass contactor that engages once the motor is up to speed. This eliminates efficiency losses in the soft start and, more importantly, allows for a smaller and less expensive design as the soft start does not have to be rated for continuous duty.
Soft starts are usually applied when a (relatively) large motor is run on a (relatively) small power system. In other words, if a single motor's full load power is equal to 25% or more of the rated capacity of the transformer feeding it, then unacceptable voltage sag results when the motor is started at full voltage. A soft start will eliminate this problem and will allow motor full load to equal transformer full load. (25% figure given above is a ballpark number, if others in the forum have more specific info please post it)
As well, soft starts may be applied to systems where it is desirable to reduce the mechanical shock of full voltage starting by gradually ramping up to speed.
Finally, soft starts may be used on large motors (>1000hp) to increase the # of allowable starts per hour. Heating is the limitation for # of starts in large motors. By limiting starting current you reduce the heating significantly and may obtain more starts per hour.
I hope this helps.