K - Poker Dictionary
Kansas City, or Kansas City lowball, is a low only game played for a deuce to seven low.
The highest unpaired card in your hand that doesn't participate in a straight or flush - i.e., the card that does not contribute to the strength of your hand except by itself. For example, if you hold AA743, you have a pair of aces with a 7 kicker. Five card hands - straights, flushes, and full houses, - don't have kickers per se. In games with community cards, kickers are especially important, because it's easy for two players to make similar hands. For example, if you hold A8 and someone else holds A7, and the flop is AK642, you have your opponent out-kicked. Your hand is AAK86 while theirs is AAK76. And you both lose to the guy playing 53 off suit under the gun.
A "kill" game is one in which a player may place an extra bet, causing the betting limits to go up for just that hand. The player posting the bet is the "killer," and the hand is considered a "kill pot." The player is said to have "killed the pot" for the amount of the kill. The exact details depend on the local rules and on the game.
As examples, here are the rules for three kill games I've played in (all in San Diego). In the kill hold'em game, any player who wins two pots in a row is required to kill by posting a blind small bet on the subsequent hand, with the limits doubled for that hand. In a kill high-low split game, any player who scooped a pot larger than a certain size was required to kill the subsequent pot. And in a draw game, any player could kill any pot for an arbitrary amount after looking at their first two cards. These are just examples, the details vary from cardroom to cardroom.