A "rage quit" refers to a player leaving a game prematurely. Simply put, on is so angry that he just walks away.
Rage quits (rq for short) are particularly common in online games with a strong focus on team play and competition. For example, there are comparatively many so-called "rage quitters" in Call Of Duty or Fifa, whereas they are rather rare in slow role-playing games.
In most cases, a rage quit builds up slowly. There is often a trigger, followed by a phase in which the player gets more and more upset. At some point, the player finally explodes, which then usually ends in ragequitten. Because of this creeping process, a ragequit can often be distinguished relatively well from a simple "disconnect".
There are an infinite number of reasons for ragequitting. Often it is more the perception or attitude of the player in the corresponding situation than real problems in the game. No matter if it's a few bad rounds in a row, supposedly incompetent teammates, death by the same player over and over again, lags and bugs or as a reaction to an insult in chat. Anyone who is relatively easily inflamed at the moment will find a reason to leave the game prematurely. Not seldom accompanied by flying keyboards, mice or controllers.
Depending on how seriously you take a game, some gamers find a Rage Quit rather amusing and take it as a reason to provoke a teammate even further.
If, on the other hand, you are very involved in the game, you see real chances of winning and there is a lot at stake, a Rage Quit is not appreciated by the team, as it is very stupid for the teammates in team-based games if they have to play the rest of the game outnumbered. Game makers also often punish rage quitters for this reason, in order to keep the game experience high for the community and fellow players in the long run.