Let’s start with what professional cuddling IS NOT:
It is NOT prostitution. Nor is it a substitute for a licensed massage therapist.
Now that we have that out of the way:
Professional cuddling is a completely platonic (i.e. non-sexual) type of touch therapy. Here in America, we live in a touch-starved nation. Professional cuddling allows strangers to meet and experience the many benefits of touch without entering into a personal relationship.
Some articles on the importance of touch/cuddling:
Psychology Today: The Importance of Cuddling
The New York Times: The Power of Touch, Especially for Men
Some videos that show professional cuddling way better than I could ever describe it: