First you need to understand how One Shot (also called AF-S or Single Shot Focus) and AI Servo (aka AF-C or Continuous Focus) work.

One Shot is intended for stationary subjects. When you press the button, the system starts focusing and as soon as focus is achieved, it stops, locks and gives you "focus confirmation". (More about focus confirmation below.) It really doesn't matter whether you release the button or not, once AF achieves focus and locks. However, if things change... if you or the subject moves and distances change... you must lift off the button and then reapply pressure to cause the camera to re-focus in One Shot mode.

AI Servo is for use with moving subjects primarily, but also can be used with stationary (with some limitations, unless BBF is used). When you press the button focusing starts and it continues to update as long as you hold the button. AI Servo doesn't stop and lock... it keeps updating focus as distances change. There is no "focus confirmation" with AI Servo. When you think about it, this makes sense since AF never stops and locks. Some people find lack of focus confirmation a little problematic... but you can get used to working without it. You need to learn how the AF system performs, how long it takes to focus, so that you can trust the camera & lens... and trust yourself.

"Holding the button" can refer to either a half-press of the shutter release or the "back button". Which "back" button is used varies by brand and model.... some Canon have an "AF On" button, while others that don't need to use the */AE Lock button, reassigned for BBF. I can't say about other manufacturers' cameras.

The primary reason for using BBF and deleting focus control from the shutter release button is to allow AI Servo to be used as your primary or default focusing mode. AI Servo with BBF can be used for both moving and stationary subjects. You can start and stop AF any time you wish by pressing and holding or releasing the button. With BBF and AI Servo, you are in charge of when and where the AF focuses. (Your selection of AF point(s) and how you position the point(s) decides "where".) This is a bit more work for you, but it also can greatly increase the percentage of in-focus shots you get.

With BBF and AI Servo, you're "ready for anything". The subject can start or stop moving. Doesn't matter. You don't have to pause shooting to change focus modes.

Focus and recompose, a technique that's only used with stationary subjects, cannot be done with AI Servo without BBF. But with BBF and AI Focus, after focus is achieved you can "lock" it simply by lifting off the button, then recompose. Easy!

Or, you can use BBF to "dodge" obstructions while tracking a moving subjects. Say you're focused on a subject moving past and they momentarily go behind a bush or tree or some other obstruction. With AI Servo the AF is going to want to re-focus on the obstruction and focus will be incorrect once the subject emerges from behind it. But with BBF you often can see what's about to occur and lift off the button momentarily while panning past the obstruction, then restart AF tracking by pressing the button again after the subject has cleared it.

There's another benefit of BBF and being able to use AI Servo all the time. Many modern zooms are "varifocal". This means they don't maintain focus when you change the focal length... i.e., when you "zoom" the lens. This is done to keep zooms smaller, simpler, lower cost to manufacture and allow them to be more affordable. Truly "parfocal" zooms that maintain focus even when zoomed tend to be bigger, more complex, require more precision to manufacture and need to be kept calibrated, all adding to their cost.

When you're using One Shot, any time you change the focal length of a varifocal zoom you must re-focus or your image will be out of focus. You have to lift off the button and reapply it, to cause One Shot to re-focus. However, with AI Servo mode the camera automatically and instantly corrects any loss of focus when the lens is zoomed. And BBF makes it possible to use AI Servo all the time. You don't have to do anything out of the ordinary to correct for a varifocal zoom, with AI Servo and BBF.

Do you even know if your zooms are varifocal or parfocal? If you use One Shot, it's important to know so you can use AF correctly. But if you use AI Servo mostly, it doesn't really matter. AI Servo AF automatically corrects for a varifocal zoom.

Here's a tip.... Many cameras have option of an audible "beep" for focus confirmation. Enable that. It's a bit obnoxious, I know. But, since there's no exposure compensation in AI Servo, the beep immediately tells me whenever I have my camera set to One Shot mode.... This helps keep me from accidentally shooting a bunch of action shots with the wrong focus mode. I hear it all the time... peoples' cameras "beeping".... when I'm shooting sporting events. I can pretty much guarantee you that most of their shots will miss focus (and they'll probably blame the camera & lens, even though it's the user's fault!)

Another thing that can help is to not shoot everything wide open. Stop the lens down when possible. This creates more depth of field and a deeper zone of acceptable focus, some forgiveness of minor focus error. It means becoming familiar with your lenses and how they blur down backgrounds at different apertures and distances... so you can decide how much to compromise to help AF. Stopping down a bit can help a lot when shooting fast and furious action.

Also, I use a single AF point most of the time. It's on me to keep that on the subject, right where I want the camera and lens to focus. That's by far the most accurate way to focus, whenever possible. There are times it's not possible, though I use as few additional points as possible (some cameras only give you choice of single point versus all points... my cameras have those an five other focus patterns: large and small zones, 4-point and 8-point expansion, high precision single point).

Back button focusing isn't for everyone. A landscape/architecture, posed portrait or macro photographer may never need it. But for anyone shooting action of any sorts, and especially anyone switching between stationary and moving subjects, particularly unpredictable ones, BBF can make a big difference in the number of "keepers" you get! It takes some practice and a short time to get accustomed to it... but soon becomes second nature. I've been using BBF for more than 15 years with a number of different cameras and have no plans to stop!