The “cleared for immediate take off” command, otherwise known as “Go, Go, Go!” is used when there is a lot of traffic around the specific airport and the controller needs you to take off as soon as possible.
If you are holding short and you hear your callsign and that command in the same sentence, you need to react to it very rapidly. You should increase power, get on the runway, and begin rolling without a stop right before it.
If you are lined up and you hear this command, then you should begin the take off without any delay whatsoever.
It’s mandatory that pilots know this, it helps ATC manage traffic more easily and it improves the traffic flow of the airspace.