Questions like this aren't easy to answer with as much detail as I'd like generally. Here's the basic theory behind color in organic molecules (which starch is).
All compounds can be excited electronically by electromagnetic radiation...when an electromagnetic transition is in the visible range...the compound will appear to us to be colored...Light of a given wavelength is perceived as [a particular] color. However, if that wavelength is absorbed, we perceive the complementary color...Intensely colored materials have absorptions in the visible region [of the electromagnetic spectrum]. For organic compounds, such electronic absorptions are generally [pi => pi*] or [n => pi*] transitions and involve extended [pi]-electronic systems. That is, color in organic compounds is generally a property of [pi]-structure. (1224-1225)
Streitwieser, Andrew, Clayton H. Heathcock and Edward M. Kosower. Introduction to Organic Chemistry Fourth Edition. Upper Saddle River: Prentice Hall, 1998.
Basically, the idea is that molecules, just like atoms, can get excited by photons. When this happens with visible light photons, the color that corresponds to the wavelength absorbed does not get reflected, and the combination of all the colors that do get reflected are seen by a viewer as the complementary color of that which is absorbed.
Starch molecules generally form a coiled shape. When iodine molecules and iodide ions are put in water, they form a triiodide ion complex which can slip into the inside of the coil. This apparently adjusts the pi system(s) in starch such that they begin to absorb photons in the visible light range; yellow photons maybe?
http://www.elmhurst.edu/~chm/vchembo...rchiodine.html