Anne's is the possessive form of Anne, showing something belongs to or relates to her.
It can also be a contraction of "Anne is" or "Anne has" before an adjective or a verb phrase.
There had been rain but it had stopped, and the light from a luminously clouded sky was pewter-bright, and puddles on the road were shivering in the wind, and the rooks above the trees in St Anne's Park were being tossed about the air like scraps of charred paper. John Banville
Auntie Anne's is a modern-day business miracle that never should have happened. Anne F. Beiler
I went to an amazing school in Brooklyn called St. Anne's that's a really kind of creative hot bed. Lena Dunham
Horalek is, of course, wrong to call the passages pornographic. Pornography is material intended to arouse sexual excitement, and I very much doubt that was Anne's intention when she wrote to her imaginary confidant Kitty about her journeys of self-discovery. Anne Frank
About a third of The Boleyn Inheritance (2006) by Philippa Gregory is recounted from Anne's point of view, covering the period of Henry VIII's marriages to her and to her successor Catherine Howard. Source: Internet
After a number of rejections, Emily's Wuthering Heights and Anne's Agnes Grey were accepted by a publisher, but Charlotte's novel was rejected by every publisher to whom it was sent. Source: Internet