Accrued rent expense is the tenant's side of accrued rent: rent for space the tenant has already occupied during the accounting period that has not yet been paid or entered in the records by the balance sheet date. The full treatment of both the tenant's and the landlord's sides is in that entry.
How the tenant records it
Under accrual accounting, rent belongs to the period in which the space is used, not the period in which the payment is made. If a tenant pays rent of $3,000 a month in arrears and the December payment will not be made until January 5, the books at December 31 are missing a month of cost. An accrual-type adjusting entry fixes this: debit Rent Expense $3,000 and credit Rent Payable, also called accrued rent liability, $3,000.
The debit puts the cost on the December income statement, so December profit is not overstated. The credit shows the obligation as a current liability on the balance sheet. When the tenant pays on January 5, it debits the liability and credits Cash, and no further expense is recorded in January for December's occupancy.
The phrase is sometimes used loosely for the expense line itself and sometimes for the unpaid balance. Strictly, the expense is Rent Expense and the unpaid balance is an accrued liability; "accrued rent expense" describes the amount that was added to expense through the accrual.