Let me give you the rundown on some terminology that gets thrown around a lot.
"Unlocking" simply refers to removing the lock on a phone's bootloader, which is what powers the Android OS. Unlocking the bootloader is the first step in gaining root access on your phone.
"Rooting" refers altering your phone so that it lets you, the user, have administrative permissions over the deepest processes of your phone. These permissions are often termed "Superuser" permissions since they involve processes (i.e. changing the maximum and minimum speeds of your phone's CPU) that normal owners are never allowed to change or likely are even aware of. When you're rooted, you can download apps that can take advantage of these permissions so long as you allow them to do so.
A "Recovery" is kind of like an app that lets you interface with ALL of the phone's files and is where you will install new ROMs on your phone. A recovery is always installed alongside when you initially root your phone, and just about any root guide you follow will show you how to do it.
A "ROM" is the software that runs on top of the Android OS and lets your phone boot up properly. Your One, and every other phone you've had, runs on one made by HTC. These are also made by the Android development community and can be installed from the recovery in place of HTC's ROM. When you root, you do NOT have to change the phone's ROM. With the HTC One, for example, you can root it and do nothing else if you want; you won't notice a thing different. If you want to keep Sense and all its features, you can just install apps that make use of root access and you won't notice any other changes, or you could install a Sense-based ROM that keeps the Sense UI intact. However, installing a different ROM usually keeps you from receiving OTA updates from your carrier/manufacturer.
Hope this was helpful!