Auto liability insurance pays for the damage you cause to property or people as a result of your negligence while driving (or, to be technical, while "using" the car...I recall a claim that occurred as a result of the insured hunting off the back of his truck, but that's another story). The maximum amount that the insurance company will pay is usually stated like this:
250/500/100 which means:
- $250,000 of coverage maximum for any one person's injury related to the accident
- $500,000 of coverage maximum for all injuries related to the accident
- $100,000 of coverage maximum for all property damage (not your own car, however) related to the accident
Keep in mind that any costs that your insurance company incurs to defend you in a lawsuit are IN ADDITION to these limits.
Also, liability coverage will not pay for any damage you do to your own property (officially this is called the care, custody and control rule). However, if you're driving and your spouse or kids are in the car with you when you hit a tree, they can (and probably will) file a claim and receive compensation for their injuries.
If you live in a no-fault state you'll need to consult the insurance laws in your state to determine when your liability coverage kicks in - every no-fault state is different.