As Missruth said, it's about working your muscles together vs. in isolation. It more closely mimics every day activities, which is more beneficial in the long run and helps prevent injury. For example, you might be able to bench press a lot of weight, but the next day you go to pick something up off the floor and get injured. That's because you're not doing exercises that target multiple muscles (chest, back, etc.) which is what you use when you do those daily activities. It's a much more efficient way to train.
Functional fitness would be using various muscles together. For example, a dumbbell row where you're standing, abs in, knees bent, back straight, leaning slightly forward, and your arm down (holding the dumbbell). And then you bend your arm raising your elbow toward the ceiling. You've engaged a bunch of different muscles during the exercise. As opposed to sitting down on a machine at the gym that just works one muscle/muscle group at a time.
Edited to add: When I first started out, I didn't "worry" about it per se. But it's a more efficient way to strength train-- since you're engaging lots of muscles at the same time, you can do more in less time.
I'm not sure what "functional fitness" would encompass, but you do whatever exercise you enjoy that you will do consistenly. If you like the type of workouts your son does, do them. If you like your current workouts and you feel good and they're not injruing you or hindering your progress, continue with them.
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