What is meant by debt management? Are there companies who can manage debt for you?

Well, a debt management plan helps you to pay off your debt faster by reducing the interest rates by half or more. You can consolidate your multiple debts into a single payment if you opt for a debt management plan. But usually, a debt management plan helps you to pay off a credit card debt. You can't opt for it for paying off your student loan debt, medical debt or any tax obligation.
And yes, you may find ample debt management companies who can manage debt for you. But before you approach, make sure to do a thorough research about the authenticity of the company.

Yes, you can get complete professional help by opting for a DMP or a Debt Management Plan/Program. All you have to do is pay a single monthly amount to the company and all other things are taken care of by them.

a professional debt relief program, where you need to pay a single amount to the company you enrolled with. All debt trouble are taken care of by the company.

You need to do a bit research before choosing a debt management company. Make sure you review the customer feedback, video testimonials, ratings and then decide.