|"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.
Poplar (genus Populus) is a genus of 25–35 species of deciduous flowering plants in the family Salicaceae, native to most of the Northern hemisphere.
"If you seek integrity, search first among the poplars" was a great maxim of Gerbold Ollivander, a saying that Garrick Ollivander supported based on his experience of poplar wands and their owners. It was said to be a wand to rely upon, of consistency, strength and uniform power, always happiest when working with a witch or wizard of clear moral vision.
There was a tired old joke among lesser wandmakers that no poplar wand had ever chosen a politician, but here they showed their lamentable ignorance: two of the Ministry's most accomplished Ministers for Magic, Eldritch Diggory and Evangeline Orpington, were the possessors of fine, Ollivander-made poplar wands.