This might not seem like a big difference but it will if you have a claim.
Depreciated Replacement Cost is a payment on an object for what it is worth today. Your giant TV might have cost $800 a few years ago but today it might be worth only $300. This is depreciated replacement cost.
Full value replacement cost is a payment based on what it would take to buy a new equivalent object today. For example: Your giant TV cost you $800 a few years ago. On the claim the insurance company may give you $800 because it would cost that much to buy an equivalent TV today.
Do you know which your policy has? If not check with your agent today to make sure you are properly covered!