Shi'ia Islam allows men to take temporary wives in addition to their permanent wives. Sunni Islam does not. The practice is old, based on the Shi'ite reading of Muhammad's own attempts to provide for widows. In a "mutaa," the religious term for temporary marriage, the man pays the woman up front, then pays her expenses for the duration of the marriage. The term can be as short as a night, or as long as he wants. He can end it whenever he wants to; she cannot end the marriage before the agreed-upon term without his permission.
Mutaa are "pleasure marriages" because they are not supposed to provide children. If the woman gets pregnant anyway, the man is supposed to support the child, but the religious courts in most places don't have the authority to enforce child support expectations.
Saddam Hussein had banned mutaa. Not only was he a Sunni Muslim, he was originally a secular nationalist. In Iraq today the Shi'ite majority is in power, and their distinctive practices, including temporary marriage, are back.
Temporary marriage was designed to protect widows in a society in which men would scorn widows (and divorced women) for virgins. Iraq today is producing many widows every day. The revival of mutaa is a rational solution to a serious problem. However, temporary marriage is so prone to abuse that it is not worth the cost to society. Temporary marriage takes advantage of women in trouble on terms that please men. As the Sunni critics say, temporary "marriage" is really a way of giving religious sanction to prostitution.
We probably can't stop the revival of temporary marriage in Shi'ite-dominated Iraq. That is their call, and not ours. But we can stay clear about why it is a long-term danger, even if it seems a rational solution to current problems.