It's the term people use when they don't want to be confused with "doing Pro/Am," as in, someone who takes a lesson with just a coach but isn't going to be competing with them. It also has to do with someone coaching an unpartnered dancer rather than a couple: like, I'm going to take a lesson by myself with another coach, she's just teaching me, and will dance with me a bit on the lesson too. That's a "singles" lesson, as in "Yeah, she said she'd do some single's lessons too."