You pay insurance premiums. In return, the insurance company covers the expenses if damage is incurred to your vehicle. Of course, the more claims you make, the higher your premiums will be... because insurance companies aren't exactly in the business of giving away free money. When you establish yourself as more of a liability that constantly requires their money to fix your car, they compensate by making you pay more to keep your insurance... helping offset the costs put into your repairs.
If you pay $2,000/year in insurance premiums, then you go 10 years w/o an accident, claim, whatever... they've collected $20,000 of your money and didn't have to shell out anything to you. They LIKE you... and reward you w/lower and lower premiums (1st year $2000 - no accidents, now 2nd year only $1500 - no accidents, so 3rd year only $1400, etc.)
But if you pay $2,000/year for the 1st year, but get in an accident that cost $4,000 to repair, now they are down $2,000 (minus your deductible - which is an amount you pay out of pocket on a claim before the insurance company picks up the rest of the bill). So they raise your premium to compensate. You need the insurance still though cause, heaven forbid, you total your $20,000 car the next year... now you'd have to shell out $20,000 instead of only the deductible (usually $500-$1000) and having insurance pay the other $19,000.
So if the damage is relatively cheap, it's pointless to put in a claim w/insurance because you'll end up paying out of pocket anyway (in the form of the deductible) and probably pay most of the bill yourself. You have to find out the price of a new bumper and paint job. If it's more than say $1500 worth of work... then you might consider making a claim to insurance. Otherwise... better get back to flippin burgers (j/k). Or in your case, it sounds like your parents pay your insurance, so you have zero risk of losing money.
