What is the story about the spot on Dagobah full of the Dark Side?

Question

I just watched The Empire Strikes Back, and noticed the part of the cave where the Dark Side was strong on Dagobah. What is its story? Also, Luke slew Darth Vader there, showing someone's face under the mask, but I didn't catch whose face it was.

Answer 1

It was Luke's face under Vader's mask in that vision fight. From The Empire Strikes Back script:

INTERIOR: DAGOBAH -- TREE CAVE

Luke moves into the almost total darkness of the wet and slimy cave. The youth can barely make out the edge of the passage. Holding his lit saber before him, he sees a lizard crawling up the side of the cave and a snake wrapped around the branches of a tree. Luke draws a deep breath, then pushes deeper into the cave.

The space widens around him, but he feels that rather than sees it. His sword casts the only light as he peers into the darkness. It is very quiet here.

Then, a loud hiss! Darth Vader appears across the blackness, illuminated by his own just-ignited laser sword. Immediately, he charges Luke, saber held high. He is upon the youth in seconds, but Luke sidesteps perfectly and slashes at Vader with his sword.

Vader is decapitated. His helmet-encased head flies from his shoulders as his body disappears into the darkness. The metallic banging of the helmet fills the cave as Vader's head spins and bounces, smashes on the floor, and finally stops. For an instant it rests on the floor, then it cracks vertically. The black helmet and breath mask fall away to reveal...Luke's head.

Across the space, the standing Luke gasps at the sight, wide-eyed in terror. The decapitated head fades away, as in a vision.

As to the cave and why it's evil: From 1991 up to the release of the prequels, the explanation in the Star Wars book Heir to the Empire strongly hinted that Yoda defeated a Dark Jedi at the cave sometime around the Clone Wars and it left some kind of mystical dark mark there. Now that the prequels are out and some of the timeline contradicts this history, there is an alternate explanation that 700 years before A New Hope a Yoda-like Jedi defeated a Dark Jedi at the cave.

From Wookieepedia, the events below are said to have happened in the usually non-continuity Star Wars Tales comic #16 "Heart of Darkness" (published 2003):

In 700 BBY, the Jedi Council received word that the Bpfassh system was being terrorized by several Dark Jedi. Minch was selected by the Council as a member of a team of Jedi Knights led by Master T'dai to venture into Bpfassh space and end the violence instigated by the Dark Jedi. ... The diminutive Jedi lost sight of the Bpfasshi, but his Force sense eventually guided him to a dark cave overgrown with brush. ... The shedding of the Bpfasshi's blood and subsequent death at the hands of Minch within the cave on Dagobah tainted that location with the dark side, and over time, transformed it into a focal point of malevolent Force energy.

According to Wookieepedia, this story has been placed in-continuity by The Complete Star Wars Encyclopedia (published 2008). Below are the alternate explanations given over the years.

From Heir to the Empire Chapter 9 excerpt (published 1991) (takes place 9 years after A New Hope):

Han's lip twisted. "The story is that some of their Jedi went bad during the Clone Wars and really mangled things before they stopped. Or so Mon Mothma says."

"She's right," Leia nodded. "We were still getting echoes of the whole fiasco in the Imperial Senate when I was serving there. It wasn't just Bpfassh, either--some of those Dark Jedi escaped and made trouble all throughtout the Sluis sector. One of them even got as far as Dagobah before he was caught."

Luke felt a jolt run through him. Dagobah? "When was that?" he asked as casually as possible.

"Thirty, thirty-five years ago," Leia said, her forehead creased slightly as she studied his face. "Why?"

Luke shook his head. Yoda had never mentioned a Dark Jedi ever being on Dagobah. "No reason," he murmured.

This is right after Luke thinks about the origins of the cave. After this quote, Luke visits Dagobah, including the cave, in Chapter 12 but nothing much happens from the perspective of this question. Note that this was published before the prequels so the Clone Wars are erroneously placed at 26 to 21 years before A New Hope. George Lucas changed the Clone Wars to take place 22 to 19 years before A New Hope.

According to a forum discussion, there is further explanation. I cannot confirm the below quotes since I no longer own the referenced media. This forum discussion seems to cover all sides and should be useful to read.

Vision of the Future (published 1998) (takes place 19 years after A New Hope):

"Me, he left mostly alone. I'm still not sure why, unless he thought he might need my knowledge of ports and spacelanes to make his escape. Or perhaps he simply wanted an intact mind left aboard who could recognize his power and greatness and be properly frightened by it. We headed across the spacelanes, dodging or avoiding the forces gathering against him. I thought up scheme after scheme to defeat him as we traveled, none of which ever made it past the planning stage for the simple reason that he knew about each of them almost before I did. I got the feeling that my pitiful efforts greatly amused him. Finally, for reasons I still don't entirely understand, we made for a little backwater system not even important enough to make it onto most of the charts. A planet with nothing but swamps and dank forests and frozen slush. A planet named Dagobah. I don't know if the Dark Jedi expected to be all alone down there. But if he did, he was quickly disappointed. We'd barely stepped outside the ship when we spotted a funny-looking little creature with big, pointed ears standing at the edge of the clearing where we'd put down. He was a Jedi Master named Yoda. I don't know whether that was his home, or whether he had just flown in specially for the occasion. What I do know is that he was definitely waiting for us." - Jorj Car'das

Star Wars Insider magazine #98 Page 56 (published January/February 2008):

The official continuity is Yoda arriving on Dagobah alone, as portrayed in the deleted scene from ROTS. According to earlier scripts, when he arrives on Dagobah he emerges from his escape pod surveying the unfamiliar terrain. Yoda has never been to Dagobah before, so Yoda's battle with a Bpfasshi dark jedi as described in Heir is no longer considered part of the continuity. It is still possible that a mortally wounded dark sider made it to Dagobah after a confrontation with Yoda but that the battle did not take place there.

Answer 2

The Thrawn Trilogy has Leia tell Luke about a Dark Jedi that was hunted down and killed on Dagobah by Jedi sometime before the rise of the Empire (this is the event @yoda alludes to). Details are at the Wookieepedia page for Dagobah.

Luke finds an ancient remote-recall device that belonged to the Jedi when he revisited the cave (but I think before Leia tells him the story).

Basically, the death of the Dark Jedi left a "stain" in the force around the cave where he was killed.