In what kind of software/webapplication/OS can I found them ?
How can I recognize one ?
By reverse engineering the software and carefully analysing it for flaws in authentication and access control, as well as issues with memory access in native applications. It's the same process by which you'd find any other vulnerability. This is not a trivial task, and entire books have been written on the subject.
If you're looking to know the difference between a generic security vulnerability and a backdoor, the difference is the intent of the programmer who put it there. You have to find evidence and use intuition to identify if it was purposeful or not. Usually this is not a yes/no answer.
How do I prevent them ?
You basically can't. You just have to expect software to be broken and have a plan to (a) keep things up to date, and (b) deal with it should there be a breach. It's not about if, it's about when.
Is the analogy good to compare them to have root access (in a Linux way) ?
Not exactly. A backdoor is anything that provides a lesser-authorised user to gain access to something they shouldn't. The backdoor might allow full access to an unauthenticated user, or it might allow some limited access to an unauthenticated user, or it might allow an authenticated low-privilege user to gain access to something at a higher privilege level.
Any more relevent informations about them.
There isn't much, really. Backdoors are just intentional faults put into code to give someone access outside of the normal security model.