Your premium is the amount you pay Allstate either twice a year, or in installments throughout the year.
Your deductible is the amount of money you've agreed to pay out-of-pocket when you make a claim covered by your policy.
For instance, let's say you get into an accident and the repairs to your car are going to cost $1,500. If you've set your deductible at $500, then you'll pay the first $500, and we'll pay the remaining $1,000 to get your car fixed and back on the road. Alternately, if your accident results in, say, $500 worth of damage (or less), you'll pay for all of the repairs, as those costs fall within the amount of your set deductible.
A lower deductible means you'll be spending less out-of-pocket and we'll be covering more of the repair costs after an accident. So a lower deductible means a higher premium (to offset that added coverage). By the same logic, increasing your deductible can usually help bring your premiums down.