Nifgaard is trying to conquer the north, the emperor has domestic problems so if he doesn't do it fast enough the opposition will kill him. In the North, only king Radovid holds any real power. He is also mad and burning magic users everywhere, using the Witcher Hunters as tools to do so. Both parties need Novigrad's money to support their war and have agents inside. Some people in the north see Radovid's madness and try to eliminate him. This last group has a conflict of interests and disagree on whether Temeria or Redania should benefit from their cover actions.
Did I forget something?
* It gets overlooked but the Conclave (if reformed) from the Witcher 2 does get referenced that Radovid's purge of magic-users is presently only limited to the Free City of Novigrad through the proxy of the Eternal Fire. He only begins a full-scale purge of the North when he no longer has any need for sorcerers.
* The situation in Velen is that the land is presented occupied by Temerian collaborators (led by the Bloody Baron) with Nilfgaard, specifically the Bloody Baron who is administrating the region while Nilfgaard prepares for its final push but maintains ties with his old allies.
* The Skellige affair is removed from the larger Nilfgaard war aside from the aborted invasion of the isles as well as their present belligerance against all visitors to it. It, however, deals with the larger theme of the game regarding the end of old ways to advance to new ones. Hjalmar represents a conservative approach, Cerys a peaceful domestication, and Bran the Younger representing aggressive modernization.
* There's a larger conflict dealing with the role of religion in society and its political misuse by various individuals. On one end, we have the Pellar, the followers of Freya, and Tamara representing its positive aspects contrasted versus its political misuse (Radovid, the Crones, the Witch Hunters, and All-God) with the overall effect showing superstition in a decidedly negative light.