The Tilonians were characterized by arches that fade from the middle of their forehead, going around their temple, and fades back away by their cheek bones. Inside the arches were a series of ridges. A common hair color among Tilonians was dark brown.
In mid-2369, the Tilonian Prime Minister was assassinated, and the government fell into anarchy. Several factions were vying for power, and doing anything they could to get their hands on weapons or technology. Some factions were resorting to torture for information. At the time, a Starfleet research team was on the planet, and were considered prime targets of the rebels. Starfleet decided to send the USS Enterprise-D to retrieve them.
Like all species, some Tilonians succumb to psychological problems, and were sent to the Tilonus Institute for Mental Disorders for treatment. This mental hospital was one of the settings – the Enterprise-D was the other – for the delusions experienced by Commander William T. Riker as he was subjected to a neurosomatic technique by Suna. (TNG: "Frame of Mind")