When a group or player will pass a group of slower golfers playing on the hole ahead. In terms of proper etiquette, it is recommended you ask permission before moving ahead.
When a player(s) invites the player(s) behind them to play ahead of them. If a group is playing slowly it is good etiquette to allow the players behind them to "play through".
(aka: "go through") passing the group in front of you (for various reasons) while they wait. Example: "The group in front of us had two very slow inexperienced players, so they let us play through.
Passing the group in front of you while they wait, generally because they are slower than you.
A situation in which a faster group is permitted to play a hole on which a slower group is playing. The slower group typically stands out of the way of the faster group, who is said to have "played through."
This is a courtesy where a slow group stand aside to allow any faster players who are immediately behind them to complete the hole first.
To pass a group of golfers who are playing ahead. Golf etiquette dictates that a slow group should allow a faster-playing group to play through.