The second season begins with everything looking pretty good in the world. Korra is chillin, having mastered airbending. Maybe she took a sabbatical to the Southern Water Tribe or something. Doesn't matter. When she returns to the City, where she now lives because Aang told her last season that she needs to stay there to keep the peace, it turns out that the Earth King has been assassinated and the military has taken over.
The King died childless so they're looking for an heir. Meanwhile they've tracked the assassin back to Republic City, allegedly he is part of the Anti-Bender Movement who took out the earth-bending King to start a revolution. The Earth Kingdom is tearing itself apart as different kings start trying to make a play for the throne. Republic City, in bureaucratic deadlock, refuses to even allow the Earth Kingdom to investigate the City.
Korra has to step in to try to smooth things over. In the epic season finale, she ultimately fails and a war breaks out between the Republic and the Earth Kingdom, troops all along the border clashing while in the Earth Kingdom wars start to break out over the throne. In the season finale she locks down into the Avatar Meditation State.
Season three begins with her in the spirit world, where Aang is showing her what's really going on. This is where the whole Harmonic Convergence thing is happening. He tells her that in two months, the Dark Spirit Vaatu will emerge from the depths of the Spirit World into the Physical World, and she - as the Avatar - must fight it. The Hundred Year War, the Fire Nation's invasion and colonization, the current crisis in Republic City, and the Earth Kingdom, and the war now breaking out is all because of this dark being awakening from its long slumber.
Korra tries in vain to convince the nations to stand down, but gets little support from the Fire Nation, who are aloof and uncaring after the HYW, and the Water Tribes aren't strong enough to intervene. (2/?)