Depending on the amplifier and speakers, a larger speaker cable (lower gauge number) can improve the damping factor of the amplifier, which improves grip on the speakers. As to why/how a cable can effect sound quality, the construction of the cable, type of insulation, and whether shielded/unshielded can also impart audible changes. It's system-dependent so YMMV.
Will increasing speaker cable AWG make a difference in sound quality?
Increasing speaker cable size (for example w/AQ the cable sizes move up in size from 15AWG to 10AWG) improve sound quality?