The term rogue is used in two main contexts within the game. Either as the pseudo-realm listed as (rogue) on the realm list or in region details, or as a status of a noble. The two terms are exchangeable, as a noble who is rogue also automatically belongs to the realm (rogue).
Regions who are not under control of any player realm are listed as members of a pseudo-realm called (rogue). While this "realm" behaves like a realm for most game mechanics, i.e. it does have a "realm and regions" list which lists all rogue regions, members of it do not attack each other, etc., it does not have an actual realm structure. There is no government and no capital, and no way to set one up. The realm exists purely as a game-mechanic and should not be treated as a "realm" in-game. Individual rogue regions do not "belong together" in any meaningful sense.
Regions can also "go rogue", through peasant revolts. This means they no longer answer to, or contribute taxes toward, another Duchy or Realm. They usually deteriorate fast, because without the guidance of any nobles, any ill effects are not treated and continue to add up. Low production and morale and, unless the region is a rural region with ample surplus, mass starvation are the usual fates of rogue regions.
There are several ways that a noble can become rogue, with the main one being banned from your own realm. A rogue exists at the bottom rung of the social hierarchy, if he can even be said to not exist there at all. Outcast from society, a rogue cannot recruit a unit, nor cash bonds in any city. If a rogue is captured he can face immediate execution or deportation by the Judge of the realm he was caught in.