A deductible is the amount of money that an insured person or business must pay for loss, damage, or services before payments will be triggered by an insurer. The terms of the deductible are stated in an insurance policy. If you have a deductible, it means that you, the insured, will be responsible for any losses or payment of services up to the stated dollar amount. You will commonly see deductibles in auto insurance and health insurance policies. Usually, deductibles are defined as a dollar amount, but can also be defined as a percentage - this is increasingly common for homeowners insurance in places that are at high risk for hurricanes and weather-related damage.
Deductibles are a way for insurers to avoid the cost of processing and paying a high volume of small claims. The more risk for loss that you, the insured, agree to assume before the insurance kicks in, the lower your premium.
Example: You are in an auto accident and your car's damages are assessed at $950 in damages. If your insurance policy has a $500 deductible, you will have to pay the first $500 of the damages to your car out of your own pocket and the insurer will pay the remaining $450. Generally, once the deductible is met, any future losses that you might have during the term of that policy will be covered in full.
Businesses can also opt for deductible plans for certain types of business coverage such as workers compensation programs.
As with all insurance matters, you need to check your own policy. Insurance can vary by state law, by type of coverage, and by individual policy. It's a good idea to read your policy and to ask your insurance agent to explain any terms that you don't understand.
Hurricane and windstorm deductibles - from the Insurance Information Institute
Deductible definitions - various definitions compiled by answers.com
How deductibles and co-pays work - a discussion of health insurance from How Stuff Works