The World Cup was an international soccer competition between Earth nations.
In 2152, England qualified for the finals of the World Cup, a fact that Jonathan Archer used to try to start a conversation with his armory officer Malcolm Reed. His attempt was unsuccessful, as Reed was not that interested in football, or any other sport, for that matter. (ENT: "Minefield")
The year 2152 is not, based on the current four year cycle, a World Cup year, but it is possible that the third World War altered this pattern as the previous world wars had affected competitions in the past. It may also be that the team qualified early, as is sometimes the case, or that Archer simply referred to the Women's World Cup