ICANN is a not-for-profit international organization. It basically controls the internet. It's based in the United States. It controls things like the names of web addresses, like "yaddayaddayadda.com" or ".org"
ICANN governs over the technical and coordination aspects of the internet.
There is some controversy surrounding ICANN because of anti-American movements. People think that ICANN is too American based. Also the internet is very local based as well as being global at the same time.
There is controversy over who actually governs the internet. Basically there is a quest for control over this very powerful and ever-growing entity called the internet.
Some people think that It is controlled by the US government too directly and they think that a more unbiased party should be in control. Others think that ICANN simply serves one purpose and really does not govern the internet at all except by controlling the names of different sites and preference protocol and the like.
People who are against denationalization of ICANN say that those who do want to denationalize are the ones who want to control the internet. They are the ones with ulterior motives. ICANN serves its purpose and it hasn't crossed any lines. In the words of Paul Twomey, President and CEO of ICANN, "Its not broken; don't try to fix it."