A temporary marriage for a stipulated amount of time. A Shi'ite belief, and generally not accepted by Sunni Muslims. There is a variant verse in the Qur'an which Shi'ites used to justify this practice.
"[Ubayy] was credited with reading Q 4.24, a verse charged with significance for the Muslim law on marriage, in a variant version: fa ma sta mta`tum bihi minhunna [ila ajalin musamman]" (Abu Bakr `Abdullah b. abi Da'ud, "K. al Masahif", ed. A. Jeffery, Cairo, 1936/1355, p. 53, quoted by John Burton, The Collection of the Qur'an, 1977, p. 35)
Narrated 'Ali bin Abi Talib:On the day of Khaibar, Allah's Apostle forbade the Mut'a (i.e. temporary marriage) and the eating of donkey-meat. (Sahih Bukhari 5.527)
Narrated Abdullah:We used to participate in the holy wars carried on by the Prophet and we had no women (wives) with us. So we said (to the Prophet ). "Shall we castrate ourselves?" But the Prophet forbade us to do that and thenceforth he allowed us to marry a woman (temporarily) by giving her even a garment, and then he recited: "O you who believe! Do not make unlawful the good things which Allah has made lawful for you." (Sahih Bukhari 6.139)
Narrated Jabir bin 'Abdullah and Salama bin Al-Akwa':While we were in an army, Allah's Apostle came to us and said, "You have been allowed to do the Mut'a (marriage), so do it." Salama bin Al-Akwa' said: Allah's Apostle's said, "If a man and a woman agree (to marry temporarily), their marriage should last for three nights, and if they like to continue, they can do so; and if they want to separate, they can do so." I do not know whether that was only for us or for all the people in general. Abu Abdullah (Al-Bukhari) said: 'Ali made it clear that the Prophet said, "The Mut'a marriage has been cancelled (made unlawful)." (Sahih Bukhari 7.52)
See also: CHASTITY HOUSES
Mut'a — Marriage or legalized Prostitution? is a detailed article that provides many quotations from Shia and Sunni sources.
Articles from a Shi`a perspective:
Articles from a Sunni perspective: