iodine is more soluble in H2O in presene of I-
As iodine is non-polar molecule it has lower solubility in polar solvent (water). However, upon addition of any iodide salt, its solubility considerably increases. It can be explained by the fact that iodine reacts with I- to form a complex salt (I-3) :
I2 + KI → KI3
Since K+I-3 is a polar substance it is highly soluble in water. Therefore, KI provides higher solubility of iodine in water.