A slot, or player slot, refers to a player who started the game and all their replacements, i.e. a set of players who are considered equivalent for the purpose of the game. Almost all game mechanics are based around player slots rather than individual players; for example, all players in a slot will (unless the game is very bastard) share the same role, the same win condition, and the like. In fact, a moderator normally allows players to interact with a slot even if it's currently unoccupied due to the replacement process; for example, most moderators will allow the town to eliminate the slot of a player who has replaced out. A slot is typically only occupied by one player at a time.
A few common mechanics are tied to the player themself, rather than the slot; most notably, activity requirements such as prods usually apply to an individual player, being reset if the player is replaced.
The concept of a slot is particularly important in cases of rulebreaking or moderator error; moderators will need to decide whether the rulebreaking has compromised a player's slot, or just the player themselves. If extra information about a player's slot has become publicly available as a consequence of rulebreaking, the slot will probably need to be modkilled. However, if the rule breach only affected a player individually, rather than the slot (perhaps the player was PMed information they shouldn't have had access to), the fairest way to preserve the game is normally with a forced replacement of the player, allowing a non-compromised player to take over the slot.