The narrator is hanging out with a friend and in conversation is told about a certain belief from a place called Uqbar. Uqwhere? Exactly. So our narrator seeks to discover this place and thereby begins a sleuth-like search through books and atlases and whatnot, and nothing can be found.
It develops into years of researching a planet called Tlön. It turns out to be a fictional place believed to have been created by a group of intellectuals and other learned types.
The story covers the particulars of Tlön. From it's unusual languages (one contains no nouns), to it's style of books (every thesis is incomplete without its anti-thesis).
It gets unusual when the narrator begins to discover this fictional world seeping into the real world - a reference here, a trinket there.
How far does the seepage go?
I owe the discovery of Uqbar to the conjunction of a mirror and an encyclopedia.
Debo a la conjunción de un espejo y de una enciclopedia el descubrimiento de Uqbar.
This story, the first in his Labyrinths collection, is only about 17 pages long. While most of the story reads as a fascinating detail of the fictional planet, which has us consider such subjects as perception and knowledge, Borges surreptitiously leads us into considering the occurrence of re-written history and how easily these untruths are accepted.
It's a dense, intricate, tight narrative. If you've never read Borges, I wouldn't recommend starting with this one.