I couldn't miss the chance to practice my drawing!
... ... ...
The mysterious man, also known as the hooded figure, is a non-player character in the first Final Fantasy. He has no officially given name. He appears in Cornelia after defeating Garland at the Chaos Shrine, but talking to him yields silence and he walks out of the town.
After the Four Fiends are defeated, speaking to him at Cornelia will direct the party to the Chaos Shrine, where the man reveals the entrance to the Labyrinth of Time. He informs the Warriors of Light about the nature and rules of the Labyrinth and leaves it available for them to challenge.
During the warriors' progression through the labyrinth, the mysterious man may appear at the start of any floor to provide help in the form of additional time, items, removing random encounters for the floor, or a possible way to leave.
The mysterious man may also appear in a level's puzzle, acting as the person the Warriors of Light report to upon completion of their task. He oversees it is done correctly, and allows passage to the next floor. Alternatively, if the warriors failed, he resets the floor and forces them to re-do the puzzle.
When the Warriors of Light reach the Space in Time the mysterious man leads them to the Lord of Time, Chronodia, before disappearing. Chronodia reveals that the Labyrinth of Time is an illusion, created for the purpose of luring powerful warriors and testing their mental and physical fortitude. If successful, they face Chronodia and seek to claim her power for their own, just as Chronodia seeks to add their power into hers. After the battle, the mysterious man will remain just outside the labyrinth as before.
It is unknown if the mysterious man is an illusion created by Chronodia, a form of Chronodia herself, or a wholly separate entity who acts as her proxy.