There are a lot of ways that the rules can be violated, and there are a few different infractions that cover Game Play Errors. There are a few specialized infractions to deal with very specific problems, such as Missed Triggers of Drawing Extra Cards. But one Game Play Error is a ‘catch-all’ that applies to any violation of the rules that is not covered by a specific infraction, Game Rule Violation. If something illegal has happened within a game, and none of the other Game Play Errors apply, they a Game Rule Violation has occurred. Common examples would be paying an incorrect amount of type of mana for a spell or performing an action when a rule or effect from a card prevents you from doing so.
Game Rule Violations are unique in that the Head Judge of an event can choose to back up the game to just before the violation occurred. It is important that this should only be done if the judge feels that backing up will not significantly impact the game. Judges generally look at how much has changed and how many decisions have been made since the error took place.
It is important to note that if this error is not caught soon enough, that the game state be left as is with no backing up and no correction applied other than the application of state-based actions. Judges should also not apply other fixes to situations like these regardless of the reasoning. The written policy is very clear; you can back up or not, but don’t try to invent and apply your own fixes.
UPDATE: There are a few exceptions for “partial fixes.” These include: make a legal choice for a permanent that required a choice as it entered (if no choice or an illegal choice was made); put a card that is in the wrong zone in the correct zone (within a turn); if you failed to discard or return cards from hand to another zone, do that now; if you forgot to draw for turn, draw now.