A bondsman is a person who is bound by bond to legally assume responsibility for another person for the terms of the bond. This bond may be for debts in the event of a default by the original person, or for other responsibilities such as when an individual is bonded out of jail.
Essentially, a bondsman is a person who legally acts as a hedge against a responsibility that another person owes. That's why if someone bonds out of jail with the help of a bail bondsman and then does not appear for court they are sought by a bounty hunter. The bondsman would be required to pay money (often a substantial sum) if the person doesn't appear in court. The reason why this is done is to provide assurance that the responsibility will be taken care of, if not by the first person, then definitely by the second person. It is similar to a parent co-signing a lease on an apartment for their child. A bondsman is legally bound to the responsibility they assume by becoming a bondsman.