When your body is functionally fit, you are able to perform everyday movements in everyday situations without the pain associated with, say a bad back. For example you may be able to lift your weight in a bench press, but are you able to lift your toddler or a bag of groceries into your car without any problems? When you workout at a gym on the machines you are training your muscles to work in 1 plane with 1 stable and controlled motion.
When you train for functional fitness you work multiple muscles at one time to work together in an unstable, yet controlled environment. For example, you may stand on 1 leg while holding a dumbell and be asked to squat down and touch the dumbell to the floor in front of you, while keeping your navel sucked in to support your back and your knee not coming past the edge of your toe, then return to upright position. Try that 15 times on 1 leg and see how much different that feels from doing a typical leg press or leg extension on a machine at the gym. By standing on 1 leg, right there you are training the lateral ligaments in your ankle to stabilize you (therefore strengthening them) so that you will be less likely to sprain your ankle next time you step on an uneven surface. By holding your navel in you are training your core to support your back, therefore strengthening your core. A strong core = a strong back. What is your core? Minus your arms, legs and head from your body and what is left is your core – where the center of all your movement begins.