If you're well into your insurance claim, you might have noticed that the insurance company sometimes does not give you the full "Replacement Cost Value" (or RCV) up front. In most policies they have the right to hold back the depreciation and only give you the "Actual Cash Value" (or ACV) of an item then once you've expended the money to replace the item you can recover the depreciation. The difference between the RCV and the ACV is the held back depreciation.
For example, say you had a couch that you estimated would cost $2,000 to replace, but the insurance company only gave you $1,250 as the ACV. Once you went and replaced the couch, you found the actual RCV was $2,145.35 and you have a receipt for the item at that cost. If you have a replacement cost policy, the $895.35 difference can be recovered from the insurance company if your claim was not closed by legal negotiations and you have not yet reached the limits for the coverage in question (which in the example is the personal property coverage).
Send copies of your receipts to the insurance company documenting the difference and request a check for the held back depreciation.