If you have an ACV (actual cash value) policy, your payment will be based on the cost of buying items in similar condition to the ones you lost; depreciation will be factored into your payment. For example, if your 10 year old refrigerator is ruined in a flood, your insurance company will determine the current value based on its condition prior to the flood, and give you that amount.
If you have replacement cost insurance, your claim will cover the lesser cost of restoring items to their original condition or buying new items of like kind and quality to the ones lost; there will be no deduction for depreciation. This means, if your four-year-old TV is stolen, the claims payment you receive will allow you to buy a new TV with features as similar as possible to the stolen model. The payment you receive may not be the same as you originally paid for the TV, as a similar model is likely cheaper now.