Diplomatic points are used by nations to perform diplomatic actions.
Almost all diplomatic actions have a cost of 1 diplomatic point. The only exceptions are 'Increase relations', which has a cost of 2, and all sphere related actions, which do not cost any diplomatic points.
All nations gain a certain amount of diplomatic points per month based on their status. The base gain is 0.3 diplomatic points pr. month. Great Powers gain 100% extra, Secondary powers gain 25% extra, and uncivilized nations gain 25% less. Other than changing status, there is no way to affect the diplomatic points gain pr. month.
The maximum amount of diplomatic points a nation is able to safe up is capped at 9.0 points. All gained points gained after that point will be lost.
One can see the current amount of diplomatic points on the diplomacy tab.