If a document is made valid (in the eyes of the law), such as by being signed or sealed, it is executed.

put to death as punishment; "claimed the body of the executed traitor"

means that you and two witnesses have signed and dated your Declaration. It will remain in effect for three years unless you cancel it, execute a new declaration, or are found to be incompetent at the time that the three years expire. When your Declaration is executed that means it is legally possible for your Declaration to be used as your instructions for mental health treatments when you can't make those decisions yourself.

Carried out according to the terms of an agreement.