To answer your question we must first recognize that Iodine (I2) is an oxidant. It wants electrons so it can become 2 I-. When I2 is in the presence of aqueous base, It is still an oxidant, but the basic environment enables I2 to undergo a process called disproportionation. The resulting products are I- which is the reduced form of iodine (it is not an oxidizer anymore) and IO3- which is an even stronger oxidant than I2. The formation of the iodate ion is why we shouldn't add iodine to basic solution. For safety details see the material safety data sheet (MSDS) in the link below.
http://dept.harpercollege.edu/chemistry/msds/Potassium%20Iodate%20Soln%20ScienceLab.pdf
