Guinan is from a long lived humanoid species from El-Auria. She traveled around the galaxy after her people were conquered by the Borg. She has a close relationship with the Enterprise captain Jean Luc-Picard. We learn in "Time's Arrow" that this is actually where she and Picard first met, although the Picard from the future remembers it differently until the future Picard meets up with the past Guinan. Got it?
Guinan has many gifts, first and foremost being a great listener. In fact, in one episode she claims to come from a species of listeners. Working in Ten-Forward as the main barkeep, she senses when someone is suffering an internal conflict, sometimes even imposing on the surprised brooding soul. The Captain, Counselor Troi, Dr. Crusher, and Ensign Ro have all gleened something from their conversations with her. She has helped them find that inner epiphany that they otherwise would have failed to recognize.
She also seems to possess a sixth sense, being able to discern when things aren't quite right. In "Yesterday's Enterprise," after the ship had gone through a time distortion, she was the only one who sensed that things arent' the way they were supposed to be. This is supposed to be a ship of exploration and peace, not war, she informs Picard. Good thing in this time line Jean Luc's relationship with Guinan is still of a close personal nature, for he trusts her intuition and orders a change of plans that sets them back on course toward the time distortion.
She also has a past relationship with the Q Continuum, primarily the one who's been a constant source of aggravation for the crew. Guinan reveals "I knew it was you" to him when he and Picard suddenly show up in Ten-Forward after the captain had been missing from the ship for several hours. When Q, out of spite for his offer of being their guide through the universe is rejected, sends the ship hurling into uncharted space, Guinan warns the captain to turn around immediately. It is this area of space where the Borg originate and unfortunately for several crew members, Picard fails to heed her warning. She becomes a valuable source of information during their encounter with the menacing species.
So here's to the best barkeep in all the Federation!