The Queen of the Visitors is the ruler of the Visitors. This title is only used by Visitors, and never when humans are present; humans only know Anna as the Visitor High Commander. The only Queen seen thus far is Anna (although Lisa was referred to by this title once, she has not yet assumed the position) and is a skilled and cunning manipulative leader who has shown leadership of the Visitors through Bliss. As Anna is the only queen shown in the series thus far, it is not known if her methods are typical of Visitor Queens. There has been no mention of a king. The queen has the ability to mate and produce offspring such as V soldiers ("Welcome to the War"). The Visitor Queen appears to function like the queen of an insect colony in addition acting as a monarch, replenishing the ranks of the Visitors by laying clutches. It is not established if any other royal or noble titles (such as "prince", "princess", "duchess", etc.) exist, as Lisa has only been described as Anna's daughter.
It is not clear what the connection between the positions of Queen and High Commander is. "High Commander" may be a separate office that Anna happens to hold in addition to her royal title, or she may simply have fabricated the title after seeing that most human governments are elected democracies and republics.
As with Earth monarchies (and insect colonies), the position of Queen appears hereditary, as Lisa is being groomed to be Anna's successor.
Queens can only be hatched from "queen eggs". The fact that both Diana and Anna have only one active daughter suggests that only one queen egg is allowed to mature at a time (although Anna kept a queen egg in reserve in case Lisa rebelled). Queens cannot breed until they develop their "breeding skin", which enables them to successfully mate and lay a clutch. It is possible that queens develop their ability to project bliss around the same time.
Another unusual feature of Visitor queens is that they possess detailed knowledge of every aspect of the Visitors and Visitor technology- both Anna and Diana possessed technical knowledge that outstripped all but their most brilliant engineers, each designing technological innovations seemingly on their own.