Being rooted means the ability to run elevated privilege commands, like the "admin" account on your computer. It gives you write access to restricted files and folders(think modding). On Windows, it's called "administrator" and on Linux, it's called "superuser" or "su" for short.
It'd be the equivalent of Dell selling you a computer with the administrator account locked out, and your account set as a "user". We don't allow computer manufacturers to do this but for some reason it's ok for smartphone manufacturers to do this.. it boggles my mind.
Unlocked bootloader is exactly what jspidey mentioned.
If you just wanna tether or backup apps with Titanium or simple things lime that then root is sufficient. If you wanna flash custom ROMs and do heavier mods you'd wanna unlock the bootloader which can now be done without notifying HTC.