Behalf means speaking or acting for someone. A parent can sign forms on behalf of children when they are young, but adult children can sign on behalf of their aging parents.
Some people make a distinction between the meaning of the word behalf when paired with in versus on. In behalf, they argue, is used when the meaning is in the interest of someone else, but on behalf is used when speaking for someone. For example, a medical decision would be made in behalf of the patient, and you would speak on behalf of your family. The reality is that on behalf is typically used for both meanings.