In insurance a deductible is the amount you have to pay out of pocket before the insurance policy starts paying. For example, if your automobile insurance has a $500 deductible, you will have to pay for the first $500 of repairs from an accident before insurance will start to pay.
High deductible insurance is often a good choice for someone who doesn't expect to use the insurance and has savings that they can use to cover the amount of the deductible. In this sense they self insure for the amount of the deductible and insurance only pays if they go beyond the deductible amount.
Low deductibles offer greater protection from loss but come with a higher priced premium. Generally lower deductibles are chosen by people with less savings or who have no emergency fund to handle unexpected expenses. They are also chosen in situations where a loss is expected. For example, someone expecting complicated health problems may want an insurance policy with a low deductible while someone in good health may opt to save the money by taking a larger risk associated with a higher deductible.