Redania is the last great power of the Northern Kingdoms, led by King Radovid. While the kingdom of Kovir still exists further north, only Redania has the military might to resist Nilfgaard on the continent. Radovid is a highly martial leader, and his version of social cohesion includes the extermination of elves, dwarves, mages, and probably witchers down the line. In fact, Radovid has his own secret police in the form of the zealous Witch Hunters.
Nilfgaard is an empire from the south, led by Emhyr var Emreis, the White Flame Who Dances Upon The Graves Of His Foes. Over twenty years ago, Geralt of Rivia freed the monster "Duny" from a curse, revealing him to be human. In this way, Geralt was ultimately the catalyst that led to Emhyr taking up the throne of Nilfgaard. The empire is well-equipped and disciplined, smashing most opponents aside with the cunning of Emhyr and his strategists. Nilfgaard does not follow the notions of racial purity that Radovid's Redania embraces, but does employ slave labour extensively.
Both of these factions fight in a similar style, emphasising close combat with long-bladed swords and polearms, and favouring heavy cavalry in pitched battle. As of the time of The Witcher 3, both factions are relatively equal in military power and position, although Radovid had better access to the city state of Novigrad -- a great hub of wealth and skilled labour.
Skellige is more like a confederacy than an individual kingdom. Each clan has a jarl, who is led by a central ruler, and that ruler is chosen by consensus when a previous one passes. While each clan is theoretically under the authority of the ruler, the laws and customs of Skellige allow the clans to behave relatively autonomously in practice. Skelligers are sea raiders, preferring lightning assaults over laborious pitched battle. Their sense of pride and honour is strong, to the extent that it can even overwrite compliance with feudal authority. Particularly rare monsters freely prowl the more remote islands of Skellige, and some even inhabit the mainland.
Novigrad is a free city, theoretically led by an elected council. In practice, its ways are shaped by various subfactions vying for control of its great wealth. The Church of the Eternal Fire is the most public and overtly accepted of its powers, but four major criminal gangs form an influential underworld, held together by shaky trust and compromises of necessity. Ironically, it's the criminal underworld and gang compromises that most protect the general populace from Redanian or Nilfgaardian occupation. Novigrad's population density means that monsters are few and far between, its nighttime streets threatened by thugs more than anything. Don't let your guard down, though, as monsters sometimes find creative ways to survive and thrive, even in secrecy.
Temeria is now only a memory, but was previously led by King Foltest. Its stability was brought to an end when Letho of Gullet, a Viper school witcher, assassinated Foltest and framed Geralt. Roche, a possible ally to Geralt, is secret intelligence officer formerly in service to Folest and intends to rebuild the Temerian state. Conversely, the Bloody Baron is a former Temerian soldier who is now a vassal for Nilgaard, controlling the fortress of Crow's Perch.