To take advantage of the best prices you will need to prove you are not a business traveller, en route to stansted airport, so you will need to give either yr flight numbers or yr holiday booking reference. I don't think you will need to provide this when you arrive at the station but you may be asked to provide them on your journey from the station to the airport.
Going to the airport by train is great, you can take a nap, read (even at night), play a game, or just gaze out of the window... The other caveat to buying these cheap train tickets from the station to the airport is that there must be at least two adults travelling together. But another great advantage is that children go free. All children under five go free, and then one kidover five but under 16 per grown up travelling by train to the airport.
make sure you leave enough time to get to the airport early enough to eat, shop etc, so check the times of trains from the station before you go. If you have time to kill at stansted airport you can always read a book or play a game again! As you have bought your train ticket in advance, you don't need to worry about the opening hours of london-kings-cross station.
Or maybe you meant