Raspbian
No matter how good the hardware of the Raspberry Pi is, without an operating system it is just a piece of silicon, fiberglass, and a few other materials. There are several different operating systems for the Raspberry Pi, including RISC OS, Pidora, Arch Linux, and Raspbian.
Currently, Raspbian is the most popular Linux-based operating system for the Raspberry Pi. Raspbian is an open source operating system based on Debian, which has been modified specifically for the Raspberry Pi (thus the name Raspbian). Raspbian includes customizations that are designed to make the Raspberry Pi easier to use and includes many different software packages out of the box.
Raspbian is designed to be easy to use and is the recommended operating system for beginners to start off with their Raspberry Pi.
Debian
The Debian operating system was created in August 1993 by Ian Murdock and is one of the original distributions of Linux.
As Raspbian is based on the Debian operating system, it shares almost all the features of Debian, including its large repository of software packages. There are over 35,000 free software packages available for your Raspberry Pi, and they are available for use right now!
An excellent resource for more information on Debian, and therefore Raspbian, is the Debian administrator's handbook. The handbook is available at http://debian-handbook.info.
Open source software
The majority of the software that makes up Raspbian on the Raspberry Pi is open source. Open source software is a software whose source code is available for modification or enhancement by anyone.
The Linux kernel and most of the other software that makes up Raspbian is licensed under the GPLv2 License. This means that the software is made available to you at no cost, and that the source code that makes up the software is available for you to do what you want to. The GPLV2 license also removes any claim or warranty. The following extract from the GPLV2 license preamble gives you a good idea of the spirit of free software:
"The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users….
When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for this service if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs; and that you know you can do these things."
