What is back button focusing?
BBF is an option offered by both Canon and Nikon on their DSLRs. All digital cameras focus when you push the shutter button half way. But for sports, action and wildlife that sucks. So in the late 80s Canon bowed to the pressure of the action photographers that were complaining about this by coming up with BBF. You go into the menu and find the right option to separate the focusing from the shutter button and put it on the * button on the back of the camera, which is operated by your thumb. So to take a photo you focus with the back button (*) and then snap the photo with your index finger.
Now that sounds really stupid to use two fingers when one would do if you have never tried it before, but there is a huge amount of benefits doing it that way. Canon has two focusing modes (actually three but AI Focus mode does not work well enough to be considered) AI Servo and One Shot AF. You use One Shot AF if you are photographing a stationary object. Once focus is achieved you can keep holding the shutter button half way and the focus is locked, allowing you to wait for the perfect moment or to do a focus/lock/recompose thing. For moving objects you would use AI Servo, in which the focus is continually updated on a moving object.
Now here is the problem. To switch between modes means menu diving, which means removing your eye from the viewfinder and then activating the menu. Cumbersome. With BBF you push the * button once and release it and you are in One Shot AF. Push the button and hold it and you are in AI Servo mode. No removing your eye from the viewfinder and no menu diving. This is extremely useful in situations where you have a perched bird that you are focused on and suddenly he takes flight. With BBF it is a very simple matter to change modes.
The same thing can be done with Nikons but i don't know the proper terminology.
But most photographers have been focusing by pushing the shutter button half way down most of their life so it is hard to convince most that there are real advantages to BBF. The only way you can experience the advantages is to switch to BBF and force yourself to use it for at least a week so that it becomes natural to you. For that first week you will certainly miss a few shots when your muscle memory takes over.
I learned about this at a Canon Workshop in Yellowstone about 6 years ago from a guy named Lewis Kemper who is one of Canon's Explorers of Light. Lewis worked for 12 years under Ansel Adams at Yosemite. The only bummer about switching to Sony is that Sony doesn't offer that option yet, but I am hopeful it will be offered in the future.
One of the biggest advantages of BBF for me is that if you want to focus on a subject and wait for something to happen you don't have to keep holding down the shutter button. One push and it is locked. There are other advantages but I haven't used the system in two years so I am a bit foggy.