Advantage is where the referee is playing the game on behalf of a team, and decides, on behalf of a team, what they think is or isn't an advantage, regardless of what a team thinks, wants or is actually happening.
Generally there are two types of advantage.
The first and quite rare and is as a result of a referee identifying an infringement instantly and notifying a player (generally only the #9 is notified).
The other more prevalent advantage, is the retrospective identification of an infringement, that is delayed generally due to having to be go through the refereeing committee process, then via head of that committee to communicate to players. The TV match official who is part of the committee, (but generally referees more of the game than the other officials with access to technology, however the quality of decisions are still on par with the other 3 officials despite the access to technology), may also identify an infringement. The TV match official must provide supporting evidence, that can be put to the refereeing committee for consideration, resulting in in a delayed advantage due to the slow process of evidence gathering.
The advantage call facilitates a team the opportunity to take a time waiting speculative option which generally they would not use and in most cases fails. As a result, the play goes back to where infringement was identified and play restarts after some game time loss and a rest break for the professional athletes. If the speculative play succeeds, it relieves the Referee of any obligation of enforcing a penalty for the offence that was committed so the offence will be overlooked unless it is foul play.
Advantage also automatically provided immunity to the offending team to commit a second repeated offence, deliberately and cynically without the receiving the same consequence for such an act at other times of the games. This immunity only applies when a advantage situation is inforce.
This is due to the traditional approach to the application of Laws in games which is intended to avoid the enforcement of the Laws in preference of referees coaching and actively encouraging professional players to play within the laws. It is unilaterally accepted that the application of the Laws in games is inconvenient and disruptive to the game. This does tend to result in the games laws being the most subjective in application and interpretation compared to all other sports.
As such, the referee's decision in relation to advantage can be game defining for a team or teams as they will select the level of advantage or penalty to a team without the need for the teams to compete equally during game play. The consequence of advantage on supporters is that we can't work out if we are sore winner or losers the uncomfortable reality that the referee is overly influential and prevalent at times when it should have been about two teams competing equally.
The above also provides an explanation why the majority of referees are ex-players. The need to be able to play the game on behalf of a team during the advantage period to ensure a result, as well a be able to coach professional players on the Laws during a game.