My daughter is a massage therapist who is also working on her Masterson Method certification. These are complementary therapies that work as other posters have explained.
As a horse owner, it’s important for you to make sure that the MT you engage has had training in a rigorous program. Some states have no established standards, and there are online programs that purport to turn out massage therapists in two or three weeks. A good, first-level program takes at least six months to complete, and even then graduates are only minimally qualified.
BTW, Scribbler, I suppose it’s possible that a one-day DIY workshop could provide owners with a few basic techniques, the kind that would do no harm even if applied incorrectly. But no one should get the idea that afterwards they can do what a real MT can do.
The suggestions above are all excellent–to rely on referrals from a trusted source, to observe a session in progress, and to take note of what the horses have to say about their sessions–heads dropping, deep sighs, licking and chewing, etc.
Sometimes the results of good massage work can be quite dramatic: At a show last season my daughter worked on a mare who had, until recently, been a stellar jumper. In her first class, however, she was backing off and even stopping. It turned out she had a large adhesion in a gluteal muscle, which my daughter was able to work out. The mare then went out and jumped like a dream, winning her 1.20 class. That’s an exceptional result, of course, but many horses are less stiff, freer in the shoulders, etc. after a good massage.
And yes, horses do nicker at an MT who’s done good work with them!