An Appointment of Agent for Disposition of Remains is a document where you designate who controls your funeral arrangements and handling of your remains after death. The State has a law in place listing who has priority, in Texas that is found in Health and Safety Code section 711.002 and starts with the surviving spouse, then adult children, then parents, then siblings, and so on.
The Appointment bypasses that hierarchy and allows you to choose who, in order, you want in control. The agent named must accept the appointment before they can act. This document is especially important if you want to designate someone outside of the normal list or if you want to put adult children in order of your preference as the law does not distinguish who of a group of children has priority to decide.