The Demogorgon was the nickname of the otherwise unnamed antagonist in season 1 of "Stranger Things." It is a creature hailing from a dark reflection of the world (the 'Upside Down'), which has the ability to create doors to other dimensions, and feed on inhabitants from there. Along with Dr. Martin Brenner, it serves as the main antagonist of the first Season, and is responsible for the paranormal disappearance of Will Byers, which builds up the events of the show.
Nothing is known about the origins of the Demogorgon or its home, but it was discovered by an enhanced child named "Eleven," whose abilities were originally utilized by Dr. Brenner for espionage. During her encounter with the Demogorgon, Eleven touches it, and the creature to use her contact with it to build a "Gate" to the reality she knew, and thus releasing it into her world, where it hunts animals and people. During this time, it takes a child, Will Byers, to his dimension to feed on him, but Will escapes from it and hides from it within the Upside Down. As Will's friends and family look for him, Eleven secretly joins the search, and helps them get clues about the whereabouts of Will. Meanwhile, Dr. Martin Brenner attempts to issue several cover-ups to prevent knowledge about the Demogorgon's threat.
The Demogorgon is eventually discovered during the course of the search, and while some characters focused on finding the truth behind Brenner's cover-ups, the rest try to find and eradicate the creature. The Demogorgon eventually encounters Nancy Wheeler, the elder sister of Will's friend Michael, and tries to kill and eat her. Nancy escapes from the Upside Down and, along with Will's brother Jonathan, develops theories on the creature's instincts. They later use this knowledge to lure it to them, while they stocked up on dangerous weapons and traps.
Meanwhile, Eleven and her new allies find a way to locate Will's presence in the Upside Down, and trick Brenner into letting them through the Gate to find him. The Demogorgon is engaged and severely injured by Nancy and Jonathan, and the former escapes to the Upside Down to avoid destruction. It then returns to the real world, where it encounters and kills Dr. Brenner as well as dozens of his agents, and attacks Will's friends Michael, Dustin, and Lucas, but is engaged by a weakened Eleven, who was low on energy by this time. Eleven uses her powers to restrain the Demogorgon, and releases a strong energy that presumably kills them both.
Will Byers, having been in contact with the Demogorgon, has symptoms of coughing up small creatures similar to it, implying that it had offspring through Will. Its crimes had also inspired many changes in the characters, both positive and negative. It is also unknown if it was killed in the first place by Eleven, because there was evidence that Eleven was alive somewhere, implying that it could have survived as well.
The Demogorgon can create and use dimension portals when in contact with any life form foreign to its dimension. It is also physically strong and dangerous, more so then most predators. It is also intimidating in appearance, which can cause adversaries and victims to panic.