Complex sentence: Stacking many such layers leads to non-linear filters that become increasingly global (i.e. responsive to a larger region of pixel space) so that the network first creates representations of small parts of the input, then from them assembles representations of larger areas.
Split into simpler sentences: Stacking many such layers leads to non-linear "filters" that become increasingly "global" (i.e. responsive to a larger region of pixel space). This allows the network to first create representations of small parts of the input, then from them assemble representations of larger areas.