In many card games, a round of play consists of some number of “tricks” where each player presents 1 card. Then, by some criteria, 1 player will “take” the trick.
The first person to play in a trick “leads” the trick. Usually, this person chooses a suit that must be followed or trumped. In that case, the following players must, if they can, play a card from the same suit as the leading card. This may be referred to as the “lead suit” of the trick. If the player cannot play the lead suit or the trump suit, then they may play a “slough” card, which is guaranteed not to take the trick.
In some games (as in up the river), the rules will specify that you do NOT need to “play to kill” and that may mean that you do not have to follow suit or play trump before sloughing cards. In those games, cleverly sloughing cards is a winning strategy.
Once all players have presented their card for the trick, the person who takes the trick is usually the person who has the largest value trump suit or the largest value lead suit.
Taking the trick may be generally desirable to gain points (as in pitch), or it may be generally undesirable (as in hearts).
Typically, the number of cards dealt to each player’s hand is the number of tricks in the round, and there may be multiple rounds of play.
The “Play to Kill” mechanic is common in trick-taking games, although it may have slightly different meanings. In general, play-to-kill is a rule where you must try to win the trick if possible.
Play-to-kill is frequently required for games with trump suits. In this case, there is typically a lead suit for each trick, and you must play the lead suit if you can. However, if you do not have a card in the lead suit, but you do have a card in the trump suit, then you must play a card of the trump suit. Additionally, if you have a card that will take the trick, you must play it regardless of whether you have other cards that meet the usual play criteria but would not take it. This is the way play-to-kill works in Pinochle.
Related Term: A “slough” is a play that is guaranteed NOT to take the trick at the time you play it.
In poker, you may see a “Kill Hand” triggered, which forces some lucky player to make a large blind bet. This mechanism is intended to curb reckless betting that wins by pure luck. As a group, we will not implement “Kill Hands” in our poker games until we are all experienced enough to unanimously agree on the need. If you wish to read more about this particular poker mechanic, you can do so at Wikipedia.