Why does Iowa matter?

One thing I haven't had adequately explained to me: why do the Iowa Caucuses matter?

I understand that Iowans will scream and cry and stamp their feet and throw tantrums if their privileged place as first-in-the-nation is ever revoked, which is why we're seeing the grotesquerie of a January 3rd caucus. And I understand that the national parties are willing to coddle Iowa and New Hampshire for the sake of party unity. But why on earth does any candidate treat Iowa like it means anything? The state is hardly representative of the nation as a whole - no more than Wyoming or Alaska or Hawaii or any other state whose demographic makeup is completely different from the rest of the nation. Meanwhile, a state like Pennsylvania, whose mix of urban, suburban, and rural, business and manufacturing and agricultural regions, ethnic and racial and religious and economic diversity, and nearly even red/blue split makes us far more reflective of the nation - Pennsylvania is given only a token primary, since the candidates have been selected long before they roll through here.

So Iowa likes to pretend that what they say matters. So the parties are willing to humor them. Why are the candidates acting like what they say matters, too?