A safe haven is a place of safety and security.
The Safe Haven Law is a series of state laws that allow young girls (and all women, technically) to give up their newborn children (the number of days it is acceptable to "turn over" a child varies from state to state) without fear of legal sanctions, as long as they drop off the child in a safe place such as a hospital, the police department, or a fire house. The intent was to prevent girls from simply abandoning or even killing newborns, if or when the girls felt overwhelmed or without family support.
While usually seen as a positive law, some people argue that the non-relinquishing parent does not get a say in the activities, and that the state can become partner to dishonesty against the non-relinquishing parent. In typical adoptions, both biological parents must waive their parental rights. In Safe Haven laws, neither is asked to relinquish their rights, they are just written off by law.
The term was popularised by British Prime Minister John Major, who called for the establishment of safe havens in Iraq after the First Gulf War to protect Kurdish rebels in the north of the country and Shia rebels in the south from the revenge of Saddam Hussein. His initiative led to the creation of no-fly zones in these areas.