Ask Ubuntu runs on the [Stack Exchange](http://stackexchange.com/) software. It's a bunch of proprietary software to run many Question and Answer sites, beginning with [Stack Overflow](https://stackoverflow.com/). Users can create new sites at [Area 51](http://area51.stackexchange.com/).

You can't get the software for yourself. But there are similar implementations, such as

 - http://shapado.com/

Which is, at least in the way it looks, _very_ similar to the Stack Exchange software.

See also:

 - [Stack Exchange’s Architecture in Bullet Points](http://blog.serverfault.com/post/stack-exchanges-architecture-in-bullet-points/)