Basically any time the armor soaks damage, it takes wear. If you have multiple pieces, it gets distributed around those pieces proportional to the soak values. As the example states, hard soak is removed first, and then remaining damage is compared to soft soak and balanced based on damage dealt and soak values. Also, it would be better to say "hard" and "soft" soak as deflection is no longer a thing. The armor takes damage instead of it being prevented all together. Armor values are always "Hard"/"Soft".
I can't really explain the formula any better than the wiki. Sorry. The example given is about as clear as it gets.