When Algol absorbed an amount of energy from the clashing of the cursed sword and the spirit sword (see his page for more details), he fashioned it into a body, weapons, and a massive tower, all based off the life he had eons ago. He named the spire the Tower of Remembrance, as it was a product of his memories, and nothing more than that—without the swords, his power was limited, and when it ran out, he knew everything he created would vanish like a mirage. Thus, in the plotline of Soulcalibur IV, Algol waits patiently in the Tower of Remembrance for the other fighters, knowing that they will be drawn in by its sudden appearance, confident that Soul Edge and Soul Calibur must be among them.
The tower has four stages:
Tower of Remembrance - Ancient Gate, the base of the tower, where all of the bonus characters are fought
Tower of Remembrance - Spiral of Time, one of the various chambers within the tower
Tower of Remembrance - Encounter, the summit of the tower when fighting Nightmare or Siegfried
Tower of Remembrance - Degradation, the summit of the tower when fighting Algol