To take advantage of these prices you will need to prove you are a leisure traveller, en route to the airport, so you will need to give either your flight details or your 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 give them on your travels from the station to the airport.
Going to luton airport by train is great, you can sleep, read (even at night), play travel scrabble, or just stare out of the window... The other caveat to buying these inexpensive train tickets from high-wycombe station to the airport is that there must be at least two grown ups travelling together. But another great advantage is that kids go free. All children under 5 go free, and then one child over five but under sixteen 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 end up with spare time at the 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 the station.
Or maybe you meant