When a potium-iodine-solution turns blue, what substance is it detecting?

It's a test for starch. The reagent is a mix of KI and I, which is KI3 and brown in color. Starch is a long chain of glucose molecules covalently bound together. The chains coil up into helixes. The I2 molecules become trapped inside the helixes, and the nature of the bonding between I2 and sugar molecules there gives a blue color. Such a complex of small molecules trapped inside a larger molecular framework is called a clathrate.