Sibyll Trelawney is named for a famous figure in Greek mythology – the sibyl, which is a term for a prophet, someone who predicts the future. The joke here is that Trelawney, the divination prof at Hogwarts, doesn't have any special powers. She's more of a Barnum and Bailey fraud than a divine oracle. Of course, calling her a fraud might be a bit harsh – the woman isn't evil, though she is (mostly) a hack.
A voice came suddenly out of the shadows, a soft, misty sort of voice.
"Welcome," it said. "How nice to see you in the physical world at last."
Harry's immediate impression was of a large, glittering insect. Professor Trelawney was moved into the firelight, and they saw that she was very thin; her large glasses magnified her eyes to several times their natural size, and she was draped in a gauzy spangled shawl. (6.1.60-2)
How fitting is it that Trelawney is myopic, which is a fancy term for nearsighted? Her super magnified lenses let us know that her vision is pretty bad. She can barely see what's in front of her with out some sort of aid, much less seeing the future. Aside from being a phony fortuneteller (albeit one who seems sold on her own abilities), Trelawney is pretty ridiculous. Her embrace of all things mystical makes her kind of absurd.
"Never forget that when thirteen dine together, the first to rise will be the first to die!"
"We'll risk it, Sibyll," said Professor McGonagall impatiently. "Do sit down, the turkey's going stone cold." (11.2.159-60)
This woman has a knack for angering highly rational individuals, especially other women – perhaps because Trelawney herself is so flighty and ridiculous that she gives them a bad name. Her weird fixation on death is also disturbing – she seems to find some entertainment value in predicting dire things. Or perhaps she feels that only negative predictions will come across as believable? At any rate, her one real prediction in this book is a doozy, and is actually accurate. If only Trelawney remembered it…