The vehicles in BATTLEGROUNDS are vitally important to map movement, largely because of how far apart players are often placed. Once the initial close groupings of players are dealt with, movement into the center of the map is important, as the outer limits will shrink. Additionally, unless a headshot or other body shot is directly targeted, the player won't take significant damage while moving in a vehicle, hugely increasing their longevity.
Attempting to exit a moving vehicle can result in player damage and even instant death as long as the vehicle is moving.
Tossing a Frag Grenade under a vehicle that has been flipped over can often flip it right side up (however this can also blow up the vehicle).
If a vehicle (works best with a UAZ) flips on its side on a flat surface, you can pop the tire that is in the air to flip it onto its wheels.
All drivable vehicles have poppable tires. If you exit your vehicle and don't want anyone else to drive it, it may be wise to shoot the tires of your vehicle.
Pay attention to your vehicle's health. If a vehicle sustains enough damage it can explode, resulting in serious player damage or death.
When shooting out of a vehicle as a passenger it is possible to kill/down other players that are in the same vehicle.
Be aware that other players, even enemy players, may enter a vehicle that you are driving.