The Armageddon is what happens when you pull out the Final Needle. Lucas's and the Masked Man's souls mix together, which means that one is bitter and angry, and one is pure. This causes the Dark Dragon to go into an enraged form and destroy the world. Everyone survives this, but the entire world is destroyed. You get a message after beating the game saying that the they are working on reconstructing it, into a better form without being controlled. Nobody that was killed during the course of the game is brought back to life either. Hinawa, Claus and the others stay killed. Nobody dies during the Armageddon however, as they are all rebuilding the Nowhere Islands.
The things that happen here are crazy. The Dark Dragon goes mad and destroys everything using the water to cause whirlpools, the stars to cause meteorites (a funny scene happens here), and the volcanoes to cause earthquakes. Then it will finally end, and that is when the game is over. You never see the Nowhere Islands reformed.
It is believed that the goal of the Dark Dragon was to make the Nowhere Islands a better place for everyone to live, instead of destroying it completely.
 Where this happened
This only happened in Mother 3. It never happened anywhere else, though it is unknown if the games all take place in the same world, just in a different time line. The only place you actually can see it happening is in Mother 3 though. The only way you can see it is by beating the Masked Man and pulling out the Final Needle. You will get the messages after moving END? in any direction for a while.