You may tell from the spelling that this is, at least in this form, a British term. It refers to a day centre which allows its users to drink alcohol on the premises (hence wet).
Such centres have been set up to reach and advise people who habitually drink alcohol in public places. Street drinkers, as they are known in social-work jargon, are mainly men in their 30s and 40s, addicted to alcohol, often homeless and with mental health problems, who are frequently rejected by mainstream health or social services because they are aggressive and disruptive and unwilling to stop drinking.
The idea of wet day centres (also called wet centres) is to provide a safe place as an alternative to spending the day on the street, where drinkers run the risk of arrest. Centres provide easy access to support and advice aimed at solving all their problems, not only to reducing their reliance on alcohol, which is usually a symptom of deeper troubles.
Though the idea of wet day centres has been around since the 1970s, there are as yet only half a dozen or so of them in the UK. It’s not clear how old the term is, but it became more widely known as the result of a survey on practical help for street drinkers commissioned by the King’s Fund and the Government’s Homelessless Directorate and published in December 2003.
The building is one of a handful of wet day centres in Britain, open to help homeless and vulnerable people by providing an area where chronic drinkers can consume alcohol.
The Guardian, 4 Feb. 2004
The goal of the new “wet” center is to get chronic drinkers off the streets and away from harm, and to reduce the enormous public resources they use up in jail and emergency rooms, said Bill Hobson, executive director of the Downtown Emergency Service Center.
Seattle Post-Intelligencer, 26 Mar. 2003