What results in a player being offside?

A player is considered to be offside when they are in an offside position at the moment the ball is played to them by a teammate. Specifically, a player is deemed to be in an offside position if they are nearer to the opponent's goal line than both the ball and the second-to-last opponent (usually the last outfield player) when that teammate makes the play. This rule is designed to prevent players from gaining an unfair advantage by positioning themselves closer to the opponent’s goal than the defenders at the moment the ball is played.

Being in their own half and receiving the ball does not constitute being offside because a player is only penalized for being offside when they are in the opposing half of the field. Similarly, proximity to the sideline does not affect offside status, as the rule is concerned solely with the positioning related to the opponents and the ball. Delaying the restart of play is unrelated to offside positioning and pertains instead to different rules governing player conduct.

Thus, answering that a player is offside when they are past the last defender at the time the ball is played accurately captures the essence of the offside rule.