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ratbastid is absolutely right. A string vibrates between its two fixed endpoints, and by fretting the string, you shorten the string and change the vibrating length and therefore the pitch.
In theory an open string vibrates between the two points exactly where it leaves the nut (at the headstock end) and the saddle (the bridge end). In practice though, the thickness and stiffness of the string play a part in it. Think about it this way - if you hold a ruler down against the edge of the table and pull it so it vibrates, its rotational point is a short distance from the edge of the table. The thicker and/or stiffer the ruler, the further away this point is.
The "crooked" bridge is an attempt to compensate for the different thicknesses of the strings. For this reason, thicker strings have to have more compensation than thinner strings.
Aha, you say - but then why does the compensation reduce between the wound and unwound strings? The reason is that wound strings are an attempt to reduce the stiffness of the string. The string is still thick, so gets lower-pitched notes, but because the outer layer is wound the whole thing is less stiff and therefore needs less compensation.
Does that sort of make sense?
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