Deductible

We've got two different meanings here. 

Taxes

On your taxes, a  deductible is something that saves you tax money by letting you subtract some amount (the deductible) from the amount the IRS is going to tax you on.

For example, let's say own your own business and one of your business expenses is marketing costs. This year, you pay $5,000 for advertising and you earn $40,000 in your business. If marketing is a deductible for you, you'd declare it on your tax forms, and you'd pay taxes on $35,000 instead of $40,000, because you take the $5,000 off the top.

Insurance

With insurance, a deductible is the amount you have to pay before the insurance company kicks in and offers you benefits. Accepting higher deductibles on your insurance can help you pay less in premiums every month, but you need to make sure that you can pay your deductible if you ever need to.

Let's say that you have car insurance with a $1,000 deductible. While driving down the highway, a clown car crashes into the back of your car, causing $1,500 in damage to your beloved vintage VW. You call the car insurance company and they remind you about that deductible. Yep, you're going to have to pony up $1,000 yourself and the insurance company will hand over the remaining $500.

Of course, five minutes after the transaction is completed, they raise your insurance rates massively since you're a "risk." Don't like it? Go to another insurance provider and see what they say.