Jane Ives was part of the experiment in the Hawkins National Laboratory, where she developed psychokinetic abilities. With those abilities she opened a gateway to the Upside Down, and inter-dimensional realm.
Eleven escaped the lab and found Mike, Lucas, and Dustin. The boys though that with her abilities he could find their missing friend Will. Eleven and Mike formed a bond over time. Eleven was forced to face a monster from the Upside Down to save her new friends. She was though to be lost in the Upside Down
Later she reappeared and lived in Jim Hopper's cabin. Eleven went to find herself and found other kids with powers. But missing her friends she went back to Hawkins, where she one again fought the inter-dimensional monsters.
Eleven became romantically involved with Mike, much to Hopper's dismay. The Mind Flayer from Upside Down however was seeking revenge and manifested physically in Hawkins. It was up to eleven to defeat the monster and close the portal for good. The strain was too much for her and she lost her powers due to it.
Powers & Abilities
Telekinesis: With her telekinesis, she can lift large and heavy objects. She was strong enough to pull a train car towards her. She can use it to cause harm to internal organs of people.
Levitation: Eleven can use her telekinesis power to lift herself up and levitate.
Remote viewing: Eleven has an ability to find people through remote viewing, even from other dimension only by using their picture and without meeting the person previously.
Telepathy: Eleven can use telepathy mostly along with her remote viewing so she can communicate with the person she is looking for.
Technopathy: She can use speakers to transmit sounds and voices.
Portal Manipulation: Eleven can open and manipulate portals to the Upside Down.
Biokinesis: Eleven disintegrated the Demogorgon, which could mean she can manipulate biology.
Memory Reading: When Eleven is in contact with a person in the void, she can see their memories.