A Modkill is the most serious punishment a mod can inflict on a player; forcibly killing them and removing them from the game. Due to the seriousness of the matter, modkills are seldom used except in egregious cases where a player has flagrantly broken the rules, and a modkill is necessary for the integrity of the game to continue. Generally, a mod would prefer to seek out a replacement sooner than a modkill, as even one extra death can throw off the balance of a game, regardless of alignment.
Occasionally a modkill is necessary late in a game, when a player disappears and nobody is willing to replace them.
Oftentimes a moderator will "punish" the side who committed the offense; for instance, if a townie posts their role PM to get the town to avoid lynching them, a moderator might not only modkill the player, but end the day without a lynch, thus depriving the town access to their biggest scumhunting tool for the day. Likewise a mafia player who communicates OOT with non-scumbuddies might be modkilled, and the game continues, allowing the town to spend their day's lynch piecing connections with the newly-flipped player.