Quirrel is an inquisitive, up-beat explorer, fascinated by the myths of Hallownest for reasons he cannot explain. While he remains a simple observer, he is wise of the land's dangers and has some skill with a nail.

Lore

Before the fall of Hallownest, Quirrel used to be Monomon’s apprentice. When Monomon became a Dreamer, she entrusted Quirrel with her mask, which was part of an additional protection enacted upon herself. Quirrel can be seen wearing this mask on top of his head.

In the official comic, it is shown that Quirrel ended up outside of Hallownest, causing him to lose much of his memory. He was called back to Hallownest by Monomon in order to reverse the protection placed on her. After entering the Howling Cliffs, Quirrel meets Hornet, whom he briefly fights. Hornet allows Quirrel to enter Hallownest when she recognizes Monomon’s mask.

Quirrel can initially be found at the Temple of the Black Egg, but he can be encountered in several locations around Hallownest. After helping the Knight kill Monomon by removing the protection on her, he goes to the Blue Lake to see the source of the rain in the City of Tears.

More facts here: https://hollowknight.fandom.com/wiki/Quirrel