Many of them actually are non-profit (Money Mgmt Int'l,
consumer credit counseling services, Etc.).
BUT that doesn't mean they work for free; it just means they try to 'break even' on the bottom line. Since they do have expenses (payroll, gas/light, phone, etc.), they do need some sort of revenue in order to pay their own bills.
Most of these places charge somewhere around $12.50/month, or something like a 15% of the monthly payment they setup for you. This just offsets their operating costs.
They also go to the creditors you're paying, and ask the creditor for their "Fair Share" of 15%. Suppose you're paying Chase $100 a month through the plan; then the company will ask Chase for $15 fair share.