Depreciation is the funds the insurance company withholds from you after they have adjusted your claim. Most people have "replacement cost value policies" which means they receive the "depreciated" funds in the form of a second check from their insurance company upon completion of the work.
There are multiple reasons your insurance company withholds these funds:
Your insurance company wants to be sure you actually have the work performed.
Your insurance company will pay you only what you spend.
You are responsible for the first portion of your claim, the deductible.