basicly it breaks down to: if ithe animal feels pain it is no longer kosher. therefore you must use a knife that is so sharp that when it slaughters the animal it doesnt flinch. if the animal flinces its felt pain... not kosher. this is why you get into all the rules on how heavy the knife has to be and how sharp it has to be.
other rules for a kosher animal are that it has to be 100% grain or natural diet. (this is why kosher beef will never have mad cow). the animal has to be able to walk to the slaughterhouse.
there are even kosher cuts of meat. some are, some arent. long story short, you really have to go out of your way to keep a kosher house, but i feel that its worth it. I find the meat to be very high quality.