To understand why back button focusing can be useful we first need to understand the differences between single and continuous autofocus modes.
With the default shutter button autofocus and our camera in a single shot autofocus mode, when we half-squeeze on the shutter button our camera acquires autofocus. No matter how much we move, or our subject moves, this focus distance is ‘locked in’ as long as our finger remains half-squeezed on the shutter button. This is the first important bit…. it means we can focus and recompose before taking the photograph.
In continuous focus mode (C, AF-C, AI servo etc. depending on your camera), when we half squeeze on the shutter button our camera acquires autofocus. But, if we move, or our subject moves, the autofocus will continuously adjust to maintain focus. This is the second important bit…. Focus and recomposing is therefore not possible because as we recompose, the autofocus continuously updates focus, thus rendering our subject out of focus.