The eagle's head and four of its wings disappear, leaving two wings in charge. That goes about as well as it ever does, and eventually the last two wings go away as well, and the body burns. At that point, Esdras wakes up. He tells the angel he's tired and weak and afraid, mostly because he hasn't had protein for several months. Now he wants god to finally say whether he likes him or not and explain the dream.
The angel does at least consent to tell him what the dream is about: the eagle is the same kingdom Daniel saw in his dream, which wasn't explained at the time, but at some point in the future, a kingdom will be the most powerful country on earth. It'll have 12 kings in a row, and the second one will reign longer than the others. That's what the feathers were. The voice was the civil war that will follow the 12th king. The eight feathers were eight new kings after the civil war. None of them will reign for long, either. The three heads are three other countries that god is going to raise up in the end times. They'll be very powerful and they'll oppress their peoples and they'll be very wicked. The last head will be one of the kings, who will die in bed, but in pain. The other two will kill each other in a sword fight. The last two feathers were a small kingdom that is full of strife. The lion is Jesus, or some variation thereof.
After getting rid of the corrupt leaders, Jesus will be nice to the people so they won't protest to much when the apocalypse arrives. The angel tells Esdras to write all this down and hide it, and eventually teach the people what he learned. But for now he's supposed to wait another 7 days and god will show him more nifty stuff.
For some reason, people are still curious about why Esdras hasn't returned, so they go out to ask him if they've offended him, because that's so hard to do. Apparently he's the last prophet, and they've got so used to being harangued all the time they sort of miss it. He promises that he hasn't abandoned them, he's just praying. He tells them to go home and says he'll be along shortly. Then he sits in the field for another week, eating flowers.