Those answers will depend on who you ask. Most people you ask #1 will tell you it's openness and the freedom associated with it to do whatever you want. But of course "Linux" does not always equal "open". Tivo, Archos, and Android are a few Linux-based devices that are based on Linux, yet have a lot of closed doors to them.

Gaining root access to a Linux operating system essentially allows you total freedom on the device to change the system in any way you want. Now the challenge is of course, you need to know "how" to change it. If you are unfamiliar with the system, then simply logging in as root does you no good. But the access is there, so you could always learn and conquer it later.