Remaining stationary on a bicycle without taking your feet off the pedals. Originally, as the name suggests, a tactic used in match sprinting on the track. In order for the rider who draws the front position to force the opponent to lead out, he or she slows down to a standstill; the other rider must then either take the lead, allowing the first to sit in their slipstream until the final seconds, or indulge in a contest to see who can stand still the longest, until one either cannot maintain the stationary position or attempts to take advantage of a wobble or inattention by the other to jump a few lengths clear. As this tactic can make a notionally two-minute race into an epic that will last all afternoon (and has, in its time, wrecked the programmes of entire race meetings), it has been strictly limited in serious racing; it is not permitted in the opening lap of the match (usually 250 or 333 m of a 1 km race), and after two minutes stationary the starter fires his pistol and the match is restarted. In addition neither rider is permitted to roll backwards to any appreciable degree; if they do so, then the match is restarted with the rider at fault taking the leading position at the start.
The practice is a great deal easier on a fixed wheel bicycle as used on the track; it is a useful skill for utility cyclists, too, particularly to avoid unclipping and reclipping into your pedals in traffic when stopping at junctions. Although bama suggests that it is easiest whilst opinting uphill, I would contend that downhill is better, particularly on freewheel, where you need to be able to rock forwards against the brake; a slight slope, such as the camber towards the kerb, can be enough to make all the difference - facing downhill also helps you accelerate away, of course. The angle of the front wheel should be as close as possible to the line you want to move away on, so on a track you would generally angle the bike down the banking with the wheel turned to the right, more or less parallel with the edge; on the road you may want your tail to be out towards the centre of the road to keep the wheel pointing forwards while you use the camber. The ideal angle between front wheel and the main plane of the bike is more like 30° than 45, but it is vital to allow the slight movements you make to bring the bike underneath you when you wobble, so it has to be enough. The bike can be leant slightly into such slope as there is to facilitate its straightening up as you pull away at maximum effort; in traffic it is best to try and hold a whole lane during your trackstand, or you may get tangled up with wing mirrors and the like when you make your lunge. You should be able to outpace a car for the first couple of seconds, giving you time to get to an acceptable riding line before they pass you.
Being able to trackstand consistently in city traffic makes it easier to obey traffic lights and such like, which keeps the rest of the world sweet, whilst remaining cool. There are few things more satisfying than screaming perfectly legally past some arsehole who has run the lights, before he even makes it to the other side of the junction. You do need to develop your jump, and get the gearing right, though.