Generically, a type of race in which competitors cover the course individually (or in cooperating teams), each starting and timed separately, with the winner being determined by the fastest elapsed time (by contrast with the simpler massed start, first across the line wins, principle). The normal format for downhill skiing, the bobsleigh/luge/skeleton family, canoeing and car rallying; a major discipline in cycling and cross-country skiing, occasionally used in athletics and motorcycling (for the Isle of Man TT races).
In cycle racing, time trialling forms a distinctive sub-discipline of road racing. It originated in the late 19th century in the UK after traditional road racing was made illegal (because it frightened the horses); it was easier to discreetly time individual riders than it was to hide a couple of hundred riding in a big bunch. The time-trialling tradition is still stronger in the UK than elsewhere; many riders ride little else. Events there are mainly run on open roads still over standard distances (10, 25, 50, 100 miles, 12 hours and 24 hours) allowing riders to compete against their own personal best times rather than each other; unfortunately this emphasis on absolute speed has led to somewhat perverse effects in that the most popular events are on dragstrip courses on dual carriageway main roads where the constant passing traffic offers additional wind assistance. They also require little technical skill (but lots of VOmax and an ability to withstand pain without losing concentration).
Elsewhere time trials are rarer (there are only a handful of significant one-off TTs on the international calendar, notably the Grand Prix des Nations, the World Championships, and the Olympic Games) but tend to play a major role in stage races (which are determined on total elapsed time over a number of separate stages) since aerodynamic effects mean that large numbers of riders finish together (with the same time) in massed-start stages; only time-trial stages and big hills are guaranteed to open up decisive time gaps. Nobody in their right mind outside the UK would dream of riding a time trial without having the roads closed for the purpose ...
As well as individual TTs team time trials for teams of two or more riders are also run. A 100 km 4-up (four riders, with at least 3 required to finish) TTT was an Olympic and World Championship event until the early 1990s, while TTT stages - all 9 or 10 riders from one team riding together, timed on the 5th rider across the line, with dropped riders given their actual times - have often featured in stage races, despite their potential for distorting the final result.