The subject of motors can be quite involved.Basically most 3 phase induction motors have 3 windings.In the majority of them these winding 'ends' are brought out into the terminal box.If you look at the rating plate it will tell you which configuration to use.Most will be designed to run at 415V in Delta, however this can lead to high start up currents due to the max. voltage being applied when the motor is stationary and there is no oppostion to current flow.This can be overcome by reducing the voltage across each winding by connecting them in Star.
However the disadvantage of this is that you have reduced the starting torque of the motor and may prove a problem in some applications.
If you can imagine the windings are called A, B and C.So winding A will have 2 ends A1 and A2 etc.Connection in Star means that A2, B2 and C2 are connected together and 3 phase is applied to A1, B1 and C1.
For Delta connection A1,C2 are together, as are A2, B1 and B2, C1.3 phase is applied to each of these pairs.
Older Star/delta starters were manual, but more recent ones are automatic, the changeover time between Star/Delta operation being determined by how the load reacts.
Hope this helps.