A rough translation of the principle of Ubuntu is "humanity towards others". Another translation could be: "The belief in a universal bond of sharing that connects all humanity".
"A person with ubuntu is open and available to others, affirming of others, does not feel threatened that others are able and good, for he or she has a proper self-assurance that comes from knowing that he or she belongs in a greater whole and is diminished when others are humiliated or diminished, when others are tortured or oppressed."-- Archbishop Desmond Tutu
As a platform based on Free software, the Ubuntu operating system brings the spirit of ubuntu to the software world.
The Ubuntu project is entirely committed to the principles of free software development; people are encouraged to use free software, improve it,and pass it on.
"Free software" doesn't mean that you shouldn't have to pay for it (although Ubuntu is committed to being free of charge as well). It means that you should be able to use the software in any way you wish: the code that makes up free software is available for anyone to download, change, fix, and use in any way. Alongside ideological benefits, this freedom also has technical advantages: when programs are developed, the hard work of others can be used and built upon. With non-free software, this cannot happen and when programs are developed, they have to start from scratch. For this reason the development of free software is fast, efficient and exciting!
You can find out more about free software and the ideological and technical philosophy behind it at the GNU website.