In the gamemember

DKP

The guild's points: how many each person has, earned and spent.

In your game: DKP

What it does: Shows the points standings: current, earned and spent. The officer gives or takes points with a reason, and under More... opens the Guild Points window, with points for the whole raid, decay and history. The points belong to the active core, or to the guild when no core is active.
Who sees it: The tab only appears when the loot system chosen in your game is DKP / Points. Only an officer changes the loot system, and the choice does not pass from one player to another: in practice, whoever sees the tab is the officer who chose DKP. Anyone opens the points window with /gos points and sees the standings, without being able to change anything.
Where to find it: In the window (J or /gos), DKP tab. The loot system, the mode and the values (points per boss, decay, starting points, cost per item) are in Settings › Loot, officer-only.

Untouched, each boss is worth 10 points, everyone starts with 0, decay is 0% and the cost per item is 0, which means off.
With Auto-award on boss kill on, the boss's points go to everyone in the raid when it dies. The one who awards is the group leader, and only if they are an officer and the raid session is running.
Decay does not run by itself: the officer presses Apply Decay, and each person loses the configured percentage of what they have, rounded.
With a cost per item above 0, whoever wins an item from the master looter pays that cost, and the raid sees the notice. It applies when the loot system is DKP and the master looter is an officer.
The standings go from whoever has the most points to the fewest; ties, by name.
Each change goes out right away to everyone in the guild with the addon and is counted only once. Only a change made by an officer is accepted.
The history keeps the last 500 changes of each core.

In the EPGP and Loot Council modes, points work as in DKP: the mode changes the name shown, not the math.
Whoever was offline when someone gained points only catches up when an officer presses Sync in the points window.
The typed name is used as is: a typo creates a new row in the standings.
Changed the active core and the points changed? Each core has its own points.