As Sophie is walking out of Market Chipping, she has a significant encounter with a turnip-headed scarecrow. A turnip is a purplish root vegetable, kind of like a potato. So imagine: a ragged, vegetable-headed scarecrow stuck into a hedge on its own. He's not even in a field, which is where scarecrows are supposed to belong. Doesn't that sound pathetic?
Now that Sophie has been turned into an old woman, she feels this odd sympathy for the scarecrow: like the scarecrow, she's out on her own and not very impressive-looking. So Sophie tells the scarecrow: "Now if I wasn't doomed to failure because of my position in the family […] you could come to life and offer me help in making my fortune. But I wish you luck anyway" (2.63).
This moment of surprising sympathy makes a huge plot difference. It turns out later that Sophie's talking actually gives the scarecrow extra life, which he uses to track down the Witch's cursed parts of the Wizard Suliman's body. The scarecrow was first enchanted by the Wizard Suliman, and eventually, when the Witch's curse ends, the parts of the scarecrow that belong to the wizard (mostly his magic and his skull) rejoin the rest of Suliman's body. So in a way Sophie accidentally helps to save Suliman's life.
But that isn't what we find symbolically significant about the scarecrow. Instead we're pointing out this image because it says a lot about how Sophie feels about herself at several stages in the novel. Here she seems to feel some odd affection for this scarecrow because she herself is feeling abandoned and homely. When the scarecrow reappears at the castle door somehow alive though, Sophie freaks out—she's not ready to admit yet that she has magic, let alone magic powerful enough to give life to a scarecrow. So she does her best to run away from the scarecrow every time she sees him.
By Chapter Twenty though, Sophie is ready for a change. The scarecrow tries to say that he means no harm, and with Calcifer's encouragement, Sophie listens to him and lets him inside. She finally admits to herself that the scarecrow "was not so frightening after all […] She rather suspected that she had just made it into a convenient excuse for not leaving the castle because she had really wanted to stay" (20.84).
Now that we've come to the end of the novel Sophie is ready to face up to her real feelings about her magic, about the scarecrow—and about wanting to stay in the moving castle. Sophie's different responses to the scarecrow over the course of Howl's Moving Castle tell us a lot about her emotional state at different points in the book.