I have read all the books and short stories and listened to a few of the forums, but I have to admit that I have only a hazy idea what the White Council actually does
There are some hints
1) They have a financial arm that trades in the stock market, manages investments
2) They have the wardens that enforce the laws of magic and defend the white council/wizards (collective security)
3) They find and train powerful practitioners in the art of Wizardry
4) They have alliances, mostly with smaller powers who they protect. They have diplomatic relations with all the significant supernatural powers and are members of the unseelee accords.
5) They are located worldwide, but the center of their power is Europe. They are fairly strong in North America, much weaker elsewhere. Less about physical territory and more about spheres of influence
6) Pyramid watching - although what purpose that services.
#3 is clearly the center of the their purpose, but #2 is also pretty high up. But judging by Harry's life, the White Council has very little impact on the day to day lives of Wizards and relatively little impact on the supernatural balance in their community. Harry upsets the balance (in a good way), but he is clearly an outsider in this respect.
But none of the above really speaks to what role the White Council has in the larger supernatural community. Maybe they are just a supernatural nation defending their own interests, but there is always this undercurrent that they (should) serve some larger purpose (humanity perhaps). Certainly they are one of the very few powers (and probably the only powerful one) that acts to some extent out of a sense of human morality. The other supernatural nations are all either very focused on their personal interests or predators or both. I suspect it was no coincidence that the first nation targeted by the outsider attack was the White Council.
Which leads to my next question - how much purpose did the original Merlin try to embed into the White Council -- and how far has the current White Council fallen short from that original vision?
And my last question - what allies did Merlin have (like Odin) that are still around - but no longer tied to the White Council's current agenda. Harry is going to need to gather strength for the final battles. Odin is one arrow in his quiver, but he needs more. Given another future book involves professional wrestler who are ex-gods, that might be another way Harry gathers powerful champions for that pivotal fight based on the outcome of that book. And Thomas is gaining reputation and power in the White Court -- which means he might eventually bring the White Court on Harry's side as well in the end days. Perhaps bigfoot will play a role as well