A royal warrant is a written notification that certain actions or powers have been granted or approved by the Crown. For example, Sir Francis Drake held a letter of marque which was a Queen's warrant.
Warrants in the SCA
While anyone can play in the SCA, there are a few things, such as signing forms or accepting payments for services, that are limited only to certain people. Anyone holding a office (Shire, Baronial, Kingdom, etc.) already has this responsibility. Warrants are generally maintained by the Kingdom officers and the requirements to get a warrant vary from Kingdom to Kingdom.