What do the various numbers attached to solar systems mean? (6.6kW, 10.7kW and so on)

These simply refer to the size of the system. The higher the number, the more solar panels there are. More solar panels mean more ability to generate electricity. It is the combined output of power that is generated from your Solar Panels Eg, 15 x 440W Solar Panels is a 6.6kW System. 15 x 440 = 6,600