The kal-if-fee (which literally translated as "challenge") was a Vulcan "passion fight" (traditionally to the death, but not necessarily) in which two Vulcan males fought for the right to mate with a certain female.
During the Vulcan mating ritual known as koon-ut-kal-if-fee, a female could claim kal-if-fee if she did not want the male arranged for her at childhood. At which point, the male arranged for her must fight the female's selected champion. If an outworlder was chosen as champion, they had the option to decline, in which case another champion would be selected. The lirpa and the ahn-woon were traditional Vulcan weapons used in the kal-if-fee. (TOS: "Amok Time")
In 2154, Enterprise NX-01 First Officer T'Pol threatened to declare the kal-if-fee when her betrothed, Koss, informed her that he intended to go through with their prearranged marriage. Koss responded by suggesting that T'Pol's "Human friend" Trip Tucker might make a suitable challenger. T'Pol consequently married Koss without calling for the kal-if-fee. (ENT: "Home")
In 2267, the Vulcan T'Pring, betrothed to Commander Spock of the USS Enterprise, claimed the kal-if-fee and chose Captain Kirk as her champion, all as part of a plot to evade her impending wedding to Spock and instead marry her preferred mate Stonn. (TOS: "Amok Time")
Females could also fight on their own behalf if they so chose. When Vorik underwent pon farr in the Delta Quadrant in 2373 and wanted to take fellow USS Voyager crewmember B'Elanna Torres as his mate, the half-Klingon female ultimately claimed the kal-if-fee and chose to champion herself. (VOY: "Blood Fever")