There was originally a company called Smart Projects SRL. They manufacture boards. Arduino LLC was the company originally founded for the Arduino project, and Smart Projects SRL manufactured the actual boards for them, because it's owned by one of the Arduino project founders, Gianluca Martino, and they were all friends. That's the backstory.
But when Arduino LLC tried to register the Arduino trademark, it turned out Gianluca Martino had registered the trademark for his own company two years prior, and not told the others. (Arduino LLC got the trademark in the USA, but were not able to register it anywhere else) This happened in 2008. At the time, they just agreed to stay friends and not make a big deal of it.
Then, last year, Smart Projects SRL made a big deal of it. They renamed their company Arduino SRL, registered arduino.org and cut their ties to Arduino LLC. This was reportedly because LLC wanted to start licensing the name to other manufacturers, but SRL wanted to keep official Arduino manufacturing to themselves. This led to the arduino.cc/arduino.org split.
That's pretty sleazy and anti-open source of them if you ask me.
If I remember correctly, Gianluca Martino's trademark registration actually predated the existence of Arduino LLC, because originally there was no company founded for the Arduino project - it was some kind of joint venture between Gianluca Martino (manufacturing, capital) and Massimo Banzi (board design).
One of the more interesting side-effects of this is that, because the Arduino libraries were written by someone else, no-one involved in the project had any experience of porting them to a completely new architecture. As AVR has gradually become slow, outdated and expensive, this has had the result that unofficial Arduino-compatible boards like Teensy are often better ports than the newer official boards.
For a long while, most people didn't understand the turmoil in the arduino market. The competing arduino.srl tried to fork the ide and even the history of the project.