What is the story of Goddess Shitala?
She is mainly worshiped in North India, West Bengal, Nepal, Bangladesh and Pakistan.
Shitala literally means cool. It is believed that the Goddess provides coolness to Her devotees who are suffering from diseases.
Here is something from Hindu Mythology
Shitala is the Bengali name for the small-pox, and for the deity who is supposed to have charge of that disease. The meaning of the word is "She who makes cold." This goddess is represented as a golden-complexioned woman sitting on a lotus, or riding on an ass, dressed in red clothes. Before an image of this kind, or morecommonly a pan of water merely, Shitala is worshipped in the hope that she will preserve her worshippers from this dire disease. In the spring of the year, the Hindus formerly inoculated their children for this disease when they were about two years of age. The Brāhman who performed the operation made presents to render Shitala propitious, and promised, in case the work was successful, to give still greater gifts. At the close of the operation the flowers that were presented to the goddess were placed in the hair of the child as a charm. On behalf of those afflicted with small-pox, offerings are made daily; and when the patient is thought to be dangerously ill, he is placed in front of an image of Shitala, bathed in, and given to drink, water that has been offered to her. Beggars go about with a stone, partly gilded, which they teach is sacred to Shitala, and, in seasons when the disease is prevalent, receive presents from the superstitious.
Here is an Another Source To Know More About Mata Shitla OMASHRAM