Once you defeat all the world bosses, you will see a cut-scene, and the middle seal in the Nexus opens up. After this point you can no longer upgrade your Soul Level by talking to the The Maiden in Black, nor will the The Monumental offer you the Friend's Ring.
You can still enter any world and farm souls or items, upgrade items, or do whatever you want without finishing the game. When you do talk to the The Maiden in Black, she will escort you to the end zone. Even from there you can return to the Nexus via the end zone Archstone, until passing through the boss fog gate, at which point you may still warp back to the Nexus using a Shard, Binding, or Miracle.
Before you complete your first playthrough, make sure you upgrade and collect as many souls as you possibly can to level up. This is primarily because once you finish the game the first time around, the next playthrough is much more difficult than the first. There are a number of things to consider before progressing to your next game cycle. Information can be found on the New Game+ page.
After you do finish the game you automatically start your New Game+. Keep in mind that you still can't upgrade your Soul Level until you beat level 1-1 again. So, you will have to carry all your souls earned defeating the last boss of this play-through, plus the souls from the end game, plus the NG+ run through level 1-1 and Phalanx, before you can spend them on levels. Alternately, spend your souls on merchant items before triggering the end.
If you have 300,000 souls and you're starting a New Game+, try not to feel too bad when you die twice in succession and lose all your souls. You should consider playing 1-1 in NG+ in Offline Mode, to prevent Black Phantom attacks, which risk losing you all those precious souls before you can spend them.
The End Game zone is a beach with some ruins, and nearby is the massive Old One. (Those with good low frequency speakers will enjoy the deep sonic effects here). The Maiden will beckon the Old One, which will come close and invite you to enter its maw-like interior.
Here then is the final boss fight against King Allant, who appears to be the captive, deformed, and despondent form of the true King Allant. Whether you feel pity for him or not, it should be an easy fight to win. Be sure you don't miss the Soulbrandt after he dies. If you have aquired Demonbrandt, then this is your last chance to make the Northern Regalia before defeating Flamelurker again in NG+. Naturally to do this requires a Shard of Archstone or your Nexial Binding to warp back, as the rear gate is closed after the Allant fight, and walking (but not warping) after the Maiden's speech will end NG. This is the very last chance you have before beginning NG+.
After you defeat King Allant, you have a choice:
All dialogue text is © Sony Computer Entertainment Inc.
Albeit brief, King Allant's dialogue offers an interesting perspective regarding the Old One's purpose:
King Allant Voiced by: Peter Marinker
Narrator Voiced by: Nikki McKenzie
Congratulations! The True Demon's Souls starts here!