I shoot with the Canon EOS 1000D (Rebel XS) and I have a 70-300mm lens for airshows.
70-300 is the focal length, which is the field of view that the lens provides. A smaller number means that you have a really wide angle, and a high number indicates a far narrower angle (which is basically a more zoomed in image).
18-55 is not enough for airshows. It will do for a general walk around lens, but not for airshows.
This link will give you a comparison of various magnifications.
I'd keep the kit lens until you save up for a better one, but do keep in mind that they're usually awful. The 75-300mm lens posted by Jordan will do you for a while until you can save up for some professional kit (if you want it), but in terms of magnification; it will do just fine. I mean, I can't speak for the actual quality of the lens, but it should be fine. Better lenses use ultrasonic motors for super fast focusing, and traditional motor lenses can be quite slow, but they still work.
To put it into perspective, a typical 70-300mm lens costs about £100. A 70-200mm lens with a 2x adapter (140-400mm lens) with stabilisation and ultra sonic motors will cost you about 10 times as much!
A bit of interesting reading for you, to get to know DSLRs:
Look at full frame cameras
Look at cropped sensor cameras (and comparisons between the two in terms of quality and images produced)
Look at videos and tutorials on how to use manual (or semi-manual) shooting modes, and how to use RAW file formats and why they're better.
If you want to see some photos with a 70-300mm lens, check out my signature and look at the Cosford airshow folder. The in-flight ones will be at about 200-300mm, and they're largely uncropped. What you see is what you get in terms of magnification.