[hceuterpe]

Phones from cell phone providers are not normally granted with a way to give "superuser" privileges, a user that gives unlimited administrator access (i.e. the user in all Linux systems included Android that can basically do anything that's possible). By lacking these privileges, you are enforced to do only certain installs, blocked from unauthorized installs, upgrades, etc. As for rooted phones vs custom flashing, You need one to be able to do the other. Custom flashing also requires root access because otherwise you are only allowed to do authorized upgrades through the Android update services provided on the phone (pushed from cell carriers).

By rooting your phone, you (forcefully) add all this functionality. The tricky thing is a Linux system (e.g. brand new Android phones) that does not have superuser privileges to start with, normally you would need to add it with those privileges, so you run into a "chicken and the egg" situation. This is why rooting phones can be complicated, and takes a bit of R&D and hacking by devs on forums such as these to find ways for particular phones.

Also selling phones not rooted inherently provides quite a bit of idiot protection so less tech savvy users don't bork their phones. This is a rather strong justification for carriers to claim you voided your warranty if you root your phone.