Virgil is a character in the game. Their purpose and motivations are unknown, but it seems like Virgil is some kind of angel confronting the protagonist with his own demons.
They look like a woman in what appears to be holy garbs, like a nun or priestess. Her clothes look very similar to the Angel statue inside Save Stations. They have buzzed hair and glowing eyes, and their skin seems grayish.
They're firstly seen in the subway with the Dog, inside the train while it leaves the station.
Lastly, they're seen in Area 1, summoning The Siren from the hole where the player must go through to reach the game's endings.
The name Virgil is probably a reference to the Divine Comedy, in which the poet Virgil is tasked with guiding Dante through the many layers of Hell.