It is a "get acquainted" party for singles, and "Meet and Mingle" is just another name for it. Just about every cruise ship has one, and it is usually on the first night, and it takes place in one of the bars. Sometimes a member of the cruise staff will be on hand to make introductions. Sometimes there won't be any representative from the ship at all. Sometimes there are free drinks. Sometimes not. It all depends on the ship and their attitude towards singles, i.e. solo travelers.
I have been to "Meet and Mingle" parties where there would be 20-30 singles, all enjoying an open bar, getting acquainted, etc., but I have also been to parties where I was the only one there! So, to repeat, it depends on the ship.
However, if you are on an organized singles cruise you can be sure that there will be someone around to make sure everyone is getting acquainted and having a good time, plus there will be refreshments.
I much prefer organized singles cruises to traveling solo...unless I am with several girlfriends.