Someone whose job or task is custodial is supposed to take care of you. A babysitter's job is custodial.
A guardian or caregiver of any kind has a custodial duty — he or she supervises and protects another person, usually a child. After a divorce, there's sometimes only one custodial parent, while the other only visits occasionally. When a criminal is sent to prison, it's often called a "custodial sentence," because the convicted person is being watched over and supervised in jail. The Latin root is custodia, "guarding or keeping."