What is a story?
Anyway, just going with the most widely accepted division for structure. Protagonist life is in a certain state (Stasis), something unexpected happens that shifts or unbalances the current state (Inciting Incident), introducing chaos, now, for the rest of the story, the protagonist will gradually move to a new state of balance which can be the same as before (restoration) or a new state (transformation).
Everything that happens from Stasis to New State is part of the main story. However, you may feel the need to introduce certain characters or plot points before the story begins. Keep in mind that background information can always be given organically as the story progresses.
Ask yourself if what you’re displaying in the prologue is utterly indispensable.
Now to examples.
Star Wars – A New Hope (Episode Four)
The movie jumpstarts with Darth Vader boarding Princess Lea’s ship. She manages to send a message out to Obi Wan Kenobi.
Later we are introduced to Luke and his Uncle Owen looking to buy new droids (Stasis). They come across R2D2, which shows the message from Lea. Luke figures Obi Wan is an eccentric hobo living nearby. Luke finds out that Obi Wan is a former jedi and the message is from the Rebellion. Agents of the Empire, tracking R2D2, come accross Like’s home while he’s away, and murder his family (Inciting Incident). Now Luke is determined to join the Rebellion against the Empire.
Note that, strictly speaking, we don’t need the scene where Darth Vader boards Lea’s ship. We can infer a lot from what we see in the story. However, the prologue does setup a smooth transition and establishes a few things, such as tone, the main external conflict, introduces Lea (which only shows up again in the second half of the movie), etc. So there’s value there, but even if you remove the prologue, the story stands on its own. If that’s not the case for you, it might be the case that either the prologue is really part of the main story, or you need to work more on the main story and not rely too much on the prologue.
Hercules (Disney Animation)
The movie starts with Hercules “christening”, all the gods come pay tribute to the first born of Zeus. Hades is clearly dissatisfied with his position in the cosmic hierarchy. Hades leaves Olympus in a fit of anger and consults with the Three Sisters. They tell him that Hercules will become an obstacle to his plan to take over Olympus. Hades sends his minions to kidnap and kill Hercules, but they screw up and Hercules survives, stripped down of his goddly status. He’s found and adopted by a mortal couple.
Many years later, Hercules is shunned and despised by everyone because he’s a clumsy teenager with superhuman strength (Stasis) and destroys everything he touches. He finds out that he was adopted and his real father is none other than the Almighty Zeus (Inciting Incident). Now he’ll spend the rest of the movie trying to reacquire his goddly status so he can return home to the other gods and not be shunned or despised anymore.
Again, strickly speaking, we don’t need that initial prologue, we learn what happened to Hercules together with him in the main story. But the movie is all the better because we get to witness all of that. We see Hades and his arrogance and resentment which will lead him to try to murder his own nephew. We get first hand account of the prophecy from the Three Sisters. We get one of the best songs in the movie (), but even if you were to watch without the first few minutes the story still stands on its own. That’s what a prologue should do.