Essentially what Thareous explained. But I'll give the gist of the story.
The outset begins with a college student who recently bought an N64 along with a few games for it at a garage sale in a common neighborhood. On his way home, he sees the house with an old man apparently holding a "garage sale" of his own. The student (known to the community as 'Jadusable') browsed around. The story explains that he looked through many strange items, including a Rorschach ink blot that resembled the shape of Majora's Mask. Eventually, he found a cartridge for the game. At this time, he did not know who the cartridge belonged to, but he bought it anyway.
When he first started, there was a file already created, and it's name was BEN. The other file was empty, so he simply created a new one. It wasn't after he he finished the game when the trouble started. When Jadusable opened his file, the setting was very eerie. He was in Clock Town, yet there was no one there, only Link. But there was something else with him, an Elegy of Emptiness statue following link around. The icing on the cape of this setting was the background music, a reverse, distorted version of the Song of Healing, accompanied by the chilling laugh of the Happy Mask Salesman. Some parts of Clock Town itself were buggy, and the statue would not stop following Link. It wasn't until after a ReDead scream was heard that the day a new day started.
The haunting went on for weeks, each time with different, frightening settings. Jadusable experienced terrible nightmares and insomnia as a side-effect. At one occasion, he opened the file of BEN, only to find that it was the most distorted and frightening of all.
One of Jadusable's first instincts was to return to the old man. But when he did, he was gone, the house had a For Sale sign on the lawn. He asked around the neighborhood to find out who BEN was. Eventually, he got an answer. Ben was a boy who previously owned the cartridge. Though apparently, he suffered a "terrible accident" that would not be explained.
Jadusable returned to his house. The next day, perhaps the most haunting incident occurred. He played the file of BEN again. This time, he appeared at the Marin Laboratory at Great Bay. He assumed Zora form and swam to the shore, but only to fin Epona, pointing in a certain direction. He swam over there to find a submerged BEN statue. As he approached it, Zora Link began to do a drowning animation, which it cannot normally do. As the Zora died, he was returned to the title screen. The two files read BEN DROWNED, explaining what the "terrible accident" was.
After a while of this, Jadusable could not stand it. After writing journals of what's happened on his computer, he put them on a flash drive and gave it to his friend. (When he put his Capture Card into his computer, the BEN spirit "infected" it as well.) He destroyed the cartridge and the computer, and was went to live with his parents.
This friend revealed the journals and videos recorded on the Capture Card to the public, and we know by this.
But it was revealed to all a hoax. There was no "haunted cartridge." The videos of the Capture Card are simply hacks to the game, nothing more. Despite this, BEN is still one of the scariest video game stories, real or not.