Mrs. Partridge is Mrs. Cadaver and Mr. Birkway's blind mother. She lives next door to Phoebe (with Mrs. Cadaver) and she is very good at reading people, even without being able to see. She reminds us of a long line of literary figures who were physically blind, but whose blindness allowed them to see deeper, greater truths. Tiresias and the Earl of Gloucester, we're looking at you guys.
Just like Sal, Mrs. Partridge uses all of her senses to understand what is going on at any given moment. She says, "'Your shoes make a particular sound and you have a particular smell'" (30.19). She can tell how old a person is simply by feeling his or her face. She's kind of magical and eerie in this way. Sal says, "Even I found this unsettling, that Mrs. Partridge could see what Phoebe was doing even though she couldn't actually see her" (30.31).
At the end of the novel, we learn that she has been responsible for leaving those secret messages on the Winterbottom doorstep. Because of this, she has been able to teach Sal and Phoebe some important life lessons and in many ways, she turns out to be a great teacher and guide.
But why do you think she left those messages?