Sybill Trelawney was a professor of Divination at Hogwarts School of Witchcraft and Wizardry. Her divination skills are lacking although she has made two successful, and very important, prophecies. She is the great-great-granddaughter of seer, Cassandra Trelawney.
In the year of 1980, Sybill convinced Albus Dumbledore for an interview regarding the new Divination Professor at Hogwarts. Dumbledore, who thought Divination was no longer needed, only gave her a chance due to her relation to Cassandra Trelawney, a well known seer. At first Dumbledore was unimpressed with her skills she showed him though as he was leaving, she made a prophecy involving the Dark Lord. Dumbledore then decided to Hire Trelawney so he could protect her from Lord Voldemort.
Prisoner of Azkaban
In 1993, Professor Trewlawney first met Harry Potter in one of her Divination lessons. She constantly predicted Harry was going to die due to numerous signs he had, thus annoying Harry.
"Sybill Trelawney has predicted the death of a student every year since she came to this school. None of them have died yet." Minerva Mcgonagall
Professor Trelawney's favourite students, Lavender Brown and Parvati Patil also joined to class the same year and were fascinated by the subject. Approaching the end of the year, she made another prophecy involving Peter Pettigrew and Lord Voldemort. 
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In OOtP, Professor Umbridge takes a disliking to Sybill, and she is sacked. However, Dumbledore lets her stay, and hires the centaur, Firenze to teach, quite to Umbridge's dismay (he being a half-human)
In 1996, Trelawney was hired to teach Divination again, but was forced to co-teach with Firenze, which she resented. She complained to the Headmaster about the arrangement many times, and warned him of the calamities soon to befall the school, but her grievances and cautions went unheard.
On one occasion, she was seen consulting her Tarot cards and talking about the Lightning-Struck Tower.
“The lightning-struck tower. Calamity. Disaster. Coming nearer all the time…” Sybill Trelawney
At another time, while she went to the Room of Requirements to hide her sherry bottles and overheard someone excitedly yelling. She questioned the person, but was thrown out of the room. Harry Potter (correctly) suspected that the person was Draco Malfoy. We learn in this book that Trelawney was the one who gave the prophecy about Harry and Vodemort. Trelawney met Harry later and revealed to him that it was Severus Snape whom eavesdropped about the prophecy about him and Voldemort.
Professor Trelawney joined the final battle at Hogwarts.
She managed to knock Fenrir Greyback out by throwing a crystal ball at his head from over the marble banisters to the Entrance Hall, after Hermione's spell hit him in time to prevent him from biting Lavender Brown. Then she shouted that she had more crystal balls for any who wanted them before heaving another from her bag and using her wand to make the ball speed across the hall and smash through a window.
Portrayals within films
Sybill Trelawney gives the apperance of being slightly batty with her large owl like glasses and dreamy voice that increases with volume as she gets excited. Harry thinks that her glasses give her the illusion of looking like a large insect
Sybill Trelawney is dramatic and mystical. However, she is quite mad when maddend.
Magical accomplishments and skills
Great-granddaughter of the celebrated Seer Cassandra Trelwaney, Sybill has made exactly 2 prophecies, one about Harry OR Neville and one about the rise of the Dark Lord.
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In popular culture
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