A character holds back anger until it can no longer be held back, and then the rage comes pouring through.
Sometimes characters have every reason to be angry, but they try to hold it back for various reasons. Sometimes, the reasons are selfish; sometimes, they are because they know it would be wrong to get angry or that blowing their top would have bad consequences (such as losing their job, getting arrested, or even getting themselves or others killed); and sometimes, the reason is just for the sake of appearances.
Eventually, there will be a last straw. It could range from a minor thing to out-and-out hitting the character's Berserk Button. But now, the flood of anger comes pouring out like water from a burst dam. It usually involves Unstoppable Rage but in some cases, it can even be Tranquil Fury. Some stories might even have this trigger a Heroic Second Wind. Also, if the character's Berserk Button is hit, this character might even be twice as berserk as usual.
Villains as well can hit this rage breaking point, typically when their schemes have become unraveled or they are losing to the hero and begin suffering a Villainous Breakdown. In such situations, they may begin Hulking Out into their One-Winged Angel form, or simply lose all calm and begin irrationally rushing the hero. It's possible the villain has shown themselves to be Affably Evil or a façade thereof, and they break as they become Ax-Crazy.
Suddenly Shouting often goes hand-in-hand with this. This response can occur after the character has Stopped Dead in Their Tracks in an attempt to control their anger.
Trope relations:
A Sub-Trope of O.O.C. Is Serious Business, You Wouldn't Like Me When I'm Angry!.
A Sister Trope to Trying Not to Cry (a tears breaking point), Beware the Nice Ones (characters who often try not to get angry).
Compare:
Break the Cutie (being sweet and nice will show a dangerous side when driven to rage)
Bullying a Dragon (in which a character or group of characters learn too late that picking on a being much more powerful than them is never a good idea, possibly one with an extremely long threshold and about to reach the end of their tether)
Do Not Taunt Cthulhu (an otherworldly, often powerful entity snaps and reveals the true extent of its power)
Enraged by Idiocy (one character has finally had enough of another's stupidity)
Fisticuff-Provoking Comment (where a character is already verbally expressing his rage before an insulting or offensive statement causes him to react with physical violence)
Moment of Weakness (driven to rage because of emotional or psychological problems the character doesn't usually have)
Not So Stoic (character holds back emotions to be stoic, and it only goes so far)
Repression Never Ends Well (a plot about repressed emotions causing trouble)
Sudden Principled Stand (a breaking point based on principles)
Suppressed Rage: (a character is trying to hold the anger back, but it's still leaking out)
Teach Him Anger (when one of the other protagonists tries to make the calm character reach this in order to make him stop being a doormat... and often regretting it afterward).
Tranquil Fury (a character is driven to rage, then becomes frighteningly calm yet undeniably angry)
Traumatic Superpower Awakening (unlock hidden powers by some breaking point)
Unstoppable Rage (when a character goes into a berserker state and attacks in a fury so bad that it is hard for them to stop)
Villainous Breakdown (a calm, collected villain is driven over the edge)
Contrast Hair-Trigger Temper (who never bothers trying to hold back), The Stoic (who almost never gets pissed in the first place) and Passive-Aggressive Kombat (a way to avoid open fights, while still being hostile).
