On her way out of Market Chipping for the first time following her transformation into an old woman, Sophie finds a dog (who later turns out to be Lettie's dog-man) tangled up in rope and tied to a staff at the side of the road. She frees the dog and takes the staff as a walking stick, since she's now about ninety years old and could use the support. So at first we think of this walking stick as a trusty support for an old woman.
But for those of you who are diehard nerds out there (like us), you may remember that in The Two Towers, the second book in J.R.R. Tolkien's Lord of the Rings series, Gandalf sneaks his magic staff into the throne room at King Théoden's hall by claiming that it's a walking stick for an old man. Obviously Gandalf is a tough old wizard—any staff he's carrying is probably not only a good crutch but also a badass magic wand.
Like Gandalf's walking stick/wizard's staff, Sophie's walking stick is also more than it appears. The difference is that Sophie doesn't recognize that her talking magic has transformed her stick into something supernatural. Since Sophie is so in denial about her own magical gift, she doesn't understand what she is doing every time she chats absentmindedly with her stick.
It's Mrs Pentstemmon who finally points out what we've all been suspecting for a while. She tells Sophie: "I like your gift […] It brings life to things, such as that stick in your hand, which you have evidently talked to, to the extent that it has become what the layman would call a magic wand." (12.54)
When Mrs. Pentstemmon mentions the power of Sophie's walking stick, what starts out as a symbol of Sophie's old age and physical frailty suddenly becomes proof of her strong magical power. And once Sophie has realized what potential her stick actually has, she starts to admit to herself that she has a lot of talent—a sign that she's overcoming her despair at being the eldest sister of three in a country where birth order can mean the difference between failure and success.