What does it mean when a massage parlor in NYC offers a 'happy ending'?

A 'happy ending' massage refers to a massage that culminates in some form of sexual activity, such as manual stimulation (slang term: 'hand-job') until the client has an orgasm. This is considered a type of prostitution.

This practice is illegal everywhere in the US where prostitution is illegal, which is almost everywhere. 'Massage parlor' is the term used for massage businesses that tend to be just a cover for the age old business of exchanging sex for money; prostitution.

It is illegal, but not uncommon.

Which is kinda dumb for them to make that illegal but drinking booze all night.