This type of damage is caused indirectly by an explosive round going off or a car exploding near you but not in direct contact with you.
Impacting Rockets and Car Cannon fire close by are where you'll most likely see 'splash damage' occur. Other weapons that have 'splash damage' are:
The area of effect for 'splash damage' depends on the round fired or vehicle explosion. Ranges are anywere between 3 and 10 Meters (+/- 1 meter).
Missiles from the Micromissile Launcher would be in the 3 Meter range while the vehicle explosion can be as large as 10+ meters encompassing everything in a huge 30 foot diameter circle.