Empire Strikes Back - Scene in Dagobah with Darth Vader

This is to reflect Luke's own darkness and how he must overcome it. He sees Vader as the face of true evil which is why it is envisioned here as him. Vader never actually appears there, physically.

When it is shown that Vader has Luke's face, this is to represent Luke's own fear of becoming as evil as Vader (if this scene occurred a movie later, it would more likely represent his fear of becoming like his father).

I'm sure Yoda, as old and wise as he is, tells Luke to go in unarmed for either his own protection against himself and/or because he knows the cave is just where a lot of dark presence is and shows hallucinations to test Luke, rather than to physically fight anything/anyone.

Lucas explains this on the Empire Strikes Back DVD commentary.

Had Luke gone into the cave with no weapons, he would not have met Vader in there.

It was a way to teach the person, by showing them what the Dark Side can bring from inside them.

Yoda said that what is in there is "only what you take with you" - Luke takes his weapons, he's aggressive - he's making the same mistakes Anakin did 25 years before, and could end up the same way. Note that it is Luke who activates his lightsaber first, not Vader - Luke is the aggressor.

A small but important note is the Yoda does not say to go in unarmed he says

"Your weapons, you will not need them"

Luke was still trusting to physical force and dominance which is a way to the dark side. Had he gone in there trusting the force (even if it had meant his life) then he would have passed the test. It shows how on a knife edge Luke actually is.

Notice he resorts to weapons later when he tries to kill the emperor in his rage and then fights Vader. He attempts to avoid the fight by hiding and negotiating but eventually loses his temper and becomes powerful enough to defeat Vader.

This is the knife edge moment but this time Luke passes, he glances at his robotic hand and observes that he is already on the way to becoming like his father and decides to throw his weapon aside. Despite being in a hostile fortress surrounded by enemies.

And it turns out to be the right move!

I read in one book that the Jedi hid a powerful Sith weapon powered by the dark side on Dagobah in the cave. Yoda the last of the Jedi counsel made Dagobah his home to keep watch over the weapon so that it wouldn't fall back into their hands. This explains why the cave was strong with the dark side, but it wasn't explained in the films.

The main plot of that film was that Luke could not alter his fate. He was destined to confront Darth Vader. Yoda keeps telling him to keep his mind focused on training, and not to worry about his friends. Which ultimately is his weakness and results in him meeting Darth Vader.

Yoda's fear is that Luke will not survive a confrontation with Darth Vader, but Yoda fails or underestimates the value of Luke's friends to save him from his fate. The goal of Yoda's training is to teach Luke that he is not ready to meet his fate.

Despite Yoda's teachings Luke doesn't seem to be afraid of his fate. Thus the phrase from Yoda "you will be". It's just another example of how Yoda is aware of Luke's fate, and Luke is ignorant of the risks.

When Luke enters the cave he sees Darth Vader. He is confronted by his fate, and when Luke strikes down Vader to reveal his own face in the mask. It demonstrates that Luke's self-confidence in his skills to beat Darth Vader will ultimately result in his death.

The idea is simple. If he fights Vader he will die, if he takes a path that leads to the dark side he will die. Staying with Yoda and finishing his training will delay his fate.

Yoda was trying to teach Luke a lesson. Luke needed to stay and complete his training. Yoda knew Luke was destine to face Darth Vader and that confrontation would kill him, because Luke wasn't ready (or worse he would turn to the dark side). Yoda was trying to protect Luke from his own fate, but at the same time understood he could do little to change his fate.

When Luke has Yoda raise his x-wing out of the swamp onto dry land, then this marks the point were Yoda gives in. He no longer seems able to steer Luke away from his fate, and Yoda dies. Yoda's death represents Luke's commitment to his fate. He can no longer continue his training. He has no choice but to face Darth Vader.

At this point. He sets on a path to full fill the vision in the cave. Face Darth Vader and die. At least, by a movie viewer's perspective at this stage in the film. That's the expected outcome, but his friends save him in the end and we learn why his fate is so closely connected to Vader.

Well I think that everyone has answered your question except for why these event happen in the cave, and why Yoda sent Luke into the cave. It was a Jedi practice to pass as a padawan to become a Jedi Knight. It works by using the force to create a mental illusion, much like what you can see in Star Wars: The Force Unleashed.

The is no threat in the cave. remember the dark side is fueled by anger, fear and hate. The imagery of the cave is the darkness within the force sensitives own heart. Luke Skywalker, son of Anakin, has the potential to become as evil and twisted as his father had become. Luke in fact sees many images of this later in the series (for those who have read the novels) when he plunges too close to the dark side.

There is a similar cave incident with one of Lukes first apprentices, Kip Durran. Go back and read that. You will understand more clearly

Shortly before entering the cave, Luke asks Yoda: "What's in there?"

Yoda replies: "Only what you take with you."

Luke begins to strap on his weapons and Yoda says, "Your weapons. You will not need those."

Against Yoda's advice, Luke brings his weapons anyway. Yoda was right -- Luke found in there what he took with him: His weapons, and in turn, his aggression and his fear -- he brought his weapons because he feared for his safety.

His fear and aggression are paths to the dark side, and so he saw himself as Vader -- because that is what would become of him based on what he brought into the cave.

Had Luke listened to Yoda and left his weapons behind, he might have seen something else.

The Force is a powerful ally. Weapons are not needed. At that time Luke was not confident in his abilities. Old habits are hard to overcome. Happiness is a warm blaster.....

Vader was present because he represented Luke's next challenge when he had to face his father in combat against the dark side... It personifies his greatest fear...

Luke's face behind the mask represents the future if he fails and turns to the dark side.

This is me channeling Master Yoda...

Everything above does sum that up for the most part. It is a powerful sixth weapon that shows one who has the force what the dark side can bring out of them. I don't care much for the expanded universe, I don't read the books are comics or watch the specials. Anyway, Yoda knows Luke's fate is to confront Vader. He knows Luke will either be seduced by the dark side, or die fighting because of insufficient training. But of course we know Luke's inevitable Fate was overcome by the improbable success of Han Solo and the rebel fleet as well as the impossible outcome of Luke bringing Vader back from the Dark Side. Luke does avoid his fate by doing the impossible and bringing back anakin skywalker. This would not have happend given Luke's understanding of his obvious similarities with Vader and how close he is to becoming him. When Luke's come back to degobah in the last film and is told by Yoda he needs no more training it is because of his own understanding of his fate and there is no more Yoda can do.