The style of debate practiced at the World Universities Debating Championship is British Parliamentary (BP for short), the most common and international style of collegiate debate in the English-speaking world.
Despite the name, there's nothing especially British about BP debate, though its origins can be traced to the British university system. The defining characteristics of the style are as follows:
15 minutes prior to each round, a "motion" is announced. Motions are drawn from a wide range of topic areas, including domestic and foreign policy, philosophy, political theory, and so on. Debaters have no idea what the motion will be until it is announced.
Four teams compete in each round, two on each side. Each team in the round has a dual burden: to rebut any arguments made by the two teams on the other side of the motion, and to do a better job of defending the motion than the other team on its own side.
Each of the four teams in a BP-style debate round comprises two members, each of whom gives one speech, usually with an upper time limit of seven minutes.
After all eight speakers have made their case, the debaters leave the room and the judges deliberate until they agree on a ranking of the teams from 1 (best) to 4 (worst). If no agreement can be reached, a majority vote is held after the time allotted for adjudication has elapsed.
Judges (ideally) rely mostly on considerations of persuasiveness in reaching their decision, though style, resolutionality, and a few other factors are also sometimes considered.
The Cape Town WUDC debating and judging manual provides additional detail about the specifics of BP debate.