ICANN is a non profit organization that is in charge of assigning domain names to different websites around the world. ICANN is run out of California in the United States. There is ongoing controversy surrounding the effects of having the internet regulated by a primarily North American organization.
Many groups and countries are pushing for the denationalization of ICANN and passing its duties off to the ITU (the International telecommunications union). This is a controversial topic. Many people believe that the way the internet works right now is perfectly fine. They also believe that splintering the duties of ICANN into the control of different countries or organizations could fragment the structure of the Internet itself. Countries could use internet issues as bargaining chips in unrelated diplomatic matters.
On the other hand, supporters of the dismantling of ICANN believe that it is time for non US groups to have control over their own web content and format. They believe that they are to a point to where they have the technical know how to operate and regulate the Internet.