Vehicles are device that are designed or used to transport people or cargo from one point to another. Vehicles are variety of categories including cars, trucks, airplanes, trains etc.
They are generally run on electric engines drawing power from on-board batteries or nuclear powered with a small reactor to the rear of the vehicle, but vehicles running on petrol also exist. The super mutant army is also said to have used some steam-powered trucks. There are numerous wrecked vehicles in the Fallout world, but functioning vehicles are now extremely rare.
The Great War was fought mainly for resources. The last resources remaining were probably depleted in the war itself. Without resources, vehicles couldn't be driven anymore. After the war, a lot of human knowledge was lost. People forgot how to tend to the high tech pre-war vehicles with their complicated electrical, oil or nuclear motors. Most books were damaged beyond all legibility by the war and many computers were destroyed due to years of neglect, and with them the documentation for these pre-war vehicles was lost. This combined with the lack of large scale primary and secondary industry meant most vehicle production/repair was largely impossible.
This does not mean that there are no old vehicles that have been kept functional or that someone out in the wastes could not have invented and adapted their own vehicles, but such instances are extremely rare outside of technologically advanced groups (i.e. groups that have overcome the struggle for basic survival and can put resources towards researching old/new technologies). A prime examples can be the New California Republic, who by 2281, have several United States military trucks repaired and in working order at Camp McCarran. At least one Vertibird VTOL aircraft is also in NCR hands, as well as several fixed wing aircraft, although it is unknown if these craft are in any working order. Another example is the Enclave, who are seen to have a large fleet of Vertibirds in their possession.