The Brechtian Cluster was a region of space containing two inhabited planets.
In 2368, all life on those planets were threatened by the Crystalline Entity. The USS Enterprise-D was able to intercept the Entity before it reached the Brechtian Cluster. (TNG: "Silicon Avatar")
The Star Trek Encyclopedia, 4th ed., vol. 1, p. 102 identified the Brechtian Cluster as a star system.
"Brechtian" is a word refering to the literary style of Bertolt Brecht