Difference between Arduino.cc and Arduino.org

The short of it is that there was a falling out within the Arduino people and now there are two groups laying claim to the "Arduino" name.

Arduino LLC runs arduino.cc. They are the steward of the Arduino IDE and libraries and own the "Arduino" trademark in the United States, and also owns the "Genuino" trademark outside of the United States. Arduino SRL (fka Smart Projects SRL) is the company that assembles(assembled) the majority of Arduino boards for Arduino LLC, runs arduino.org, and owns the "Arduino" trademark inside Italy and all of the other countries they have registered the "Arduino" trademark.

Arduino SRL recently decided that they are no longer beholden to Arduino LLC and has stopped paying licensing fees for using the Arduino name. Whether this is justified or not has not been fully tested in court yet.

This article can explain it better than I could paraphrase: http://hackaday.com/2015/02/25/arduino-v-arduino/

Relevant excerpt:

Arduino LLC [arduino.cc] is the company founded by Massimo Banzi, David Cuartielles, David Mellis, Tom Igoe and Gianluca Martino in 2009 and is the owner of the Arduino trademark and gave us the designs, software, and community support that’s gotten the Arduino where it is. The boards were manufactured by a spinoff company, Smart Projects Srl, founded by the same Gianluca Martino. So far, so good.

Things got ugly in November when Martino ... renamed Smart Projects to Arduino Srl and registered arduino.org

According to this Italian Wired article, the cause of the split is that Banzi and the other three wanted to internationalize the brand and license production to other firms freely, while Martino ... [wanted] to list on the stock market and keep all production strictly in the Italian factory.

Please take a look at The Untold History of Arduino.