Backbutton focus means pressing your shutter button no longer automatically autofocuses your camera. Instead, you control it with the AFOn button. It provides the best of manual focus, AFS, and AFC, without having to change modes on your camera.
With newer mirrorless cameras, such as the Sony a7 III, a7R III, and a9, you can program separate buttons for standard autofocus and eye AF. That's perfect for portraits and sports, where sometimes you want to rapidly switch between those focusing modes.
With many DSLRs, such as the Nikon D500, D850, Canon 5DSR, 5D Mk IV, and 7D Mk II, you can program one AFOn button to do a single autofocus point, and a second button (such as AEL) to focus with all autofocus points. That's perfect for shooting wildlife, where sometimes you need to pick out a single subject from a cluttered background, and other times you want the camera to track a flying bird against a clear sky using all the camera's autofocus points.
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INSTRUCTIONS FOR SETTING UP BACKBUTTON FOCUS: http://sdp.io/tutorial. Find the tutorial for your camera, then check the description of that video for a link directly to backbutton focus.