ACV stands for Actual Cash Value. ACV is the amount that the damaged property was worth prior to the loss.
RCV is Replacement Cost Value. RCV is what it will cost to replace that property.
The difference is depreciation. How old is that damaged carpet, table, roof? An insurer will deduct for depreciation based on the age of the item.
If you only have ACV coverage, then that is what you will get. If you think the number is low, you can haggle. But you are not entitled to get the value of brand new if you do not have RCV coverage.
Most RCV policies state that (1) they will pay ACV and then (2) they will pay RCV after the replacement cost has been incurred. The idea is to disincentivize fraud. Sometimes they will pay RCV up front anyway.
When construction is needed, sometimes the insurer will pay the contractor directly. This way the policyholder does not have to shell out RCV and wait for reimbursement.
Some RCV policies have time limits for the replacement/rebuild. In Michigan, these are enforceable. But, if the insurer denies coverage outright, it might not be able to enforce the RCV time limit. Smith v. Mich. Basic Prop. Ins. Assoc., 441 Mich. 181 (1992).