A "happy ending" is when a Oriental tantric massage ends with sexual contact called "hand relief", usually masturbation and oral sex. Happy endings can be offered to both male and female clients by massage services, but though males are the more typical customer. However, there are many "spas" are basically fronts for body massage, like the old-fashioned "massage parlour." They are often in the news for being raided and shut down -- something to keep in mind should you be tempted.
Tip-offs that the massage might include a happy ending is wording for services that seems a little off, like full body massage, body shampoo, and thigh massage, or oriental touch. Asian massage has a long time histroy and proud tradition, but it has also sometimes become a word for happy ending.