Many Wikipedians go about their Wikipedia business under the illusion that administrators are just like everyone else and do not have authority or power. This is simply false. According to Wiktionary, authority is "The power to enforce rules or give orders." By any rational definition, this applies to administrators.
To illustrate this reality, let us consider the following analogy. In the United States, it is illegal for a law enforcement officer to search your personal property (ignoring for purposes of this analogy exigent circumstances or other exceptions to the rule). This means that a police officer lacks the authority to execute a search of your personal belongings. However, should the police officer have probable cause enough to convince a judge that a search is necessary, that judge may issue a search warrant. That search warrant grants the authority, issued by the judge, derived by the constitution, and originating from "the people" who have ratified that constitution, for the officer to execute that search. The officer already has the power to do so, by virtue of the use of force, perhaps by brandishing his or her weapon.
To compare this to Wikipedia, both authority and power are very pertinent here. The power granted to administrators are the tools which empower them to enforce order, such as by blocking users. The authority administrators yield is the allowance that they execute their power, and that authority is derived by the Wikipedia community, which entrusts these users with this special responsibility.