A square wave consists of many component sinewaves, mainly of say V at the fundamental frequency F, then V/3 at 3F, V/5 at 5F, V/7 at 7F. This can continue ad infinitum, depending on the squarewave's rise time. The components are also in phase at some point in time.
So when you pass the above sinewaves through your filter, two things happen, the first is that the higher order harmonics get further attenuated, causing the rise time to increase, and secondly, the higher order sinewave progressively lag in time so the trailing edges of the square will show ringing.
Frank