The Terlina system was a remote planetary system.
After the destruction of the Omicron Theta colony in 2338, Dr. Noonian Soong and his wife Juliana re-settled on Terlina III.
In 2367, Data brought the USS Enterprise-D to this system in response to Dr. Soong's summoning signal. Lore also arrived at the system aboard a small Pakled vessel. (TNG: "Brothers", "Inheritance")
According to the script, the pronunciation for Terlina is "tur-LEE-nah". 
The identity of Soong's star system was not revealed until TNG