The angel says that he helped support Darius the Mede during his reign (who Daniel also served). But he goes on to tell Daniel that four more kings will arise in Persia, and the last of these will stir up a war with Greece. This is going to backfire terribly when a great warrior king (Alexander the Great) comes out of Greece to establish a massive empire.
But when Alex dies, his empire will be split four ways—not by his descendants, but by others.
The king of the south is going to grow in might, but one of his officers will end up gaining even more power and ruling an even bigger realm.
The daughter of the king of the south will try to make an agreement with the king of the north, but it won't fly. The offspring of the king of the south aren't going to be able to rule. The daughter and her attendants and children will all be "given up."
But "a branch from her roots"—one of her relatives—is going to rise up and fight the king of the north and win. He will carry off plunder to Egypt.
Then, there will be a brief period of peace, before the king of the north invades the land of the king of the south.
The sons of the king of the north are going to lead the massive assault. The king of the south will muster up a large army, but he's going to get defeated.
During that time, a lot of people are going to join the fight against the king of the south—including some of the more lawless Hebrews.
But Daniel says that they're going to fail (even though the king of the north himself is going to win, beating the king of the south by taking over a fortified city and successfully killing the king of the south's crack troops).
The king of the north is able to take over Judea, the beautiful land. He then attempts to offer a woman in marriage to the king of the south. But this doesn't bring any peace or political advantage to the king of the north.
The king of the north will capture many people from the coastlands, but will be taken to account by an official of some sort (probably a Roman tax-collector demanding that the king of the north pay tribute to Rome). He will finally fall and disappear (probably killed when robbing a temple to get plunder to pay off Rome, for the record).
Re-Enter Arrogant Horn Guy (This Time as a Person)
Another official (likely a tax-collector) will be sent out, but will fail in his mission (which may have been to loot the Jerusalem Temple).
Finally the big villain of these prophecies (the same as the arrogant little horn from the first vision: Antiochus IV Epiphanes) appears on the scene.
He will successfully attack and defeat his enemies, including the Jews who attempt to defend their religion and way of life. His skill at intrigue helps him succeed.
The bad king is going to keep plundering places and giving the booty to the richest people. Then, he will attack the king of the south. This time, the king of the south is going to be defeated (though not killed, apparently), with traitors from his court helping the bad king.
The two kings will now plot together, but to no effect.
King of Forts
Now, the bad king will return back to the north and prepare to attack and persecute the Jews. But actually, instead he's going to go back to the south again and get defeated there by a fleet of ships from Kittim (Rome).
So now, the real persecutions start. His armies are going to attack and desecrate the Temple in Jerusalem and the Jews' fortress.
They're going to stop the regular burnt offering given to God, and set up "the abomination that makes desolate" (probably a statue of Zeus).
The king will seduce some Jews away from fulfilling their religious duties, breaking the covenant.
The wise Hebrews will be able to help their people, but will be attacked and killed. But the persecutions the wise suffer are a way of purifying them for the times that will come later, at the end.
The king will go on doing whatever he wants. He's going to act like he's greater than any god, and will say blasphemous things about God himself.
But he's only going to prosper for a limited time period.
The king will ignore all gods, and will only pay worship to a foreign god of fortresses.
He'll continue rewarding his cronies and selling the lands he's conquered.
At the end of the chapter, the angel continues the story of the future: he says that the king of the south will fight yet another war with the bad king.
The bad king is going to invade many lands and sweep along, fighting in Judea and Egypt. Libyans and Ethiopians will join his army.
He will make his war camp between the holy mountain of Jerusalem and the sea. But eventually he'll be destroyed and utterly defeated.