The X car was built by GM as a new-wave compact car for the 80s. Variations include:
1980-85 Buick Skylark
1980-84 Oldsmobile Omega
1980-84 Pontiac Phoenix
1980-85 Chevrolet Citation
In the 1970s, GM knew it had to downsize its entire fleet of cars to that they could produce highly fuel efficient vehicles that would meet the upcoming CAFE fuel economy standards of the 80s. The full-sized (B and C body), mid-sized (A body) and specialty (E body) cars were restyled and down-sized in 1977, 1978, and 1979 respectively.
For 1980, GM produced the smallest compact cars ever made by an American car company. (i.e. Some subcompacts were already smaller.) These were the X cars: the Skylark, Omega, Phoenix, and Citation. These were the first front wheel drive cars from an American company produced on a large scale. (The Japanese were way behind on front wheel drive. Some European cars, and the Plymouth Horizon, Dodge Omni, and Olds Toronado were already front wheel drive.)
The transverse mounting of the engine and transmission allowed the cars to have modest exterior dimensions while still possessing generous interiors and trunks. Most important, they could be fitted with small 4 cylinder and 6 cylinder engines, for increased fuel efficiency. These cars are much smaller than the 1979 Skylark, Omega, Phoenix, and Nova, which allowed for much better fuel economy.
GM's goals for these cars, when it set out to design them in July 1974, were that they should be fuel efficient, roomy, safe, durable, and easily serviced (Courtesy Chilton's X-Car Manual). Needelss to say, GM achieved these goals.
All front wheel drive models introduced thereafter in the 80s were based on the X car design. This included the A-bodies (Century, Cutlass Ciera, 6000, Celebrity), the J-bodies (Skyhawk, Firenza, Sunbird, Cavalier, and Cimarron), and the N-bodies (Grand Am, Cutlass Calais, Skylark). GM even used the engines, transmissions, and suspension components when designing the Fiero. Other GM cars also were based upon this design.
Thus, the original X-car design was critical to GM in terms of its 80s and 90s car designs.