|"Is this all real? Or has this been happening inside my head?"
The topic of this article is of a real-life subject that has been mentioned "in-universe" in a canon source. The Harry Potter Wiki is written from the perspective that all information presented in canon is true (e.g., Hogwarts really existed), and, as such, details contained in this article may differ from real world facts.
Peony is a genus of flowering plants, the only genus in the family Paeoniaceae.
The Weasley family grew a peony bush in the back yard of their home at The Burrow, and, apparently, there were gnomes burrowing under it, as it was the first place from which a gnome popped up while the Weasleys were De-Gnoming the garden in the summer of 1992.