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 does 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.