Why do the women in the countryside think Ichabod is an important person? How do the young girls respond to him?

Ichabod Crane is considered an important person in Sleepy Hollow. This idea might seem strange, as Ichabod is undoubtedly ridiculous and comical by turns, but the fact remains that he's a school teacher, and school teachers were generally considered important people during Washington Irving's day. After all, school teachers were far more highly educated than the average person, and a teacher's life seemed to be filled with more leisure than the average farmer's. As such, Ichabod appears to be something of a gentleman to the humble inhabitants of Sleepy Hollow.

By extension, the women of Sleepy Hollow regard Ichabod as an ideal husband for their daughters. Along the same lines, the girls of Sleepy Hollow see the school teacher as an eligible future spouse. The exception to this rule is Katrina Van Tassel, who also happens to be the woman Ichabod is most interested in. Katrina is ultimately interested in Brom Bones, so Ichabod's expression of affection late in the story is met with a stinging rejection.