what does "no happy endings'here mean?
“Back?”
“Yeah, with my table. You need a massage.”
“I don’t want—”
“Need,” she repeated. “You may not think you want one, but trust me, you will after I get started. This one’s on the house—a welcome back gift. Therapeutic massage, Eli,” she added. “I’m licensed. No happy endings.”
“Well, Jesus.”

Question

what does "no happy endings'here mean?
“Back?” 
“Yeah, with my table. You need a massage.” 
“I don’t want—” 
“Need,” she repeated. “You may not think you want one, but trust me, you will after I get started. This one’s on the house—a welcome back gift. Therapeutic massage, Eli,” she added. “I’m licensed. No happy endings.” 
“Well, Jesus.”

Answer

Many massages are sexual in nature resulting with ejaculation as the final part of the massage.  She is saying that she is a licensed masseuse who gives quality (body relaxing) massages but not sexual ones.     A happy ending is where the person receiving the massage ejucalates (cums)

Answer

It means that she will give him a good professional massage, and will not perform any sexual services.