"Kit" isn't really a soccer thing as much as it is a British thing. Rugby uniforms and the like are also referred to as kits, generally meaning uniform or equipment. Of course Americans and Canadians are most likely to hear it in reference to soccer uniforms, as it is a term that has made its way into the soccer lexicon in North America. The word "strip" is also used interchangeably in this context.
I think "kit" can also refer to clothing generally, as the phrase "get your kit off" means take off your clothes. Feel free to correct me if I'm wrong, as I am not British.