One of the most important duties of the executor or administrator is keeping an accurate accounting of the estate assets. Prior to distribution, an executor should prepare an accounting of all of the assets and liabilities of the estate, including all sources of assets (i.e. bank accounts, refunds, sale of real estate) and all liabilities paid and still outstanding (i.e. funeral costs, unpaid credit cards, medical bills).
The accounting must accurately show what went into the estate, what went out, and what is left to be distributed amongst the heirs.
An account is necessary whenever there are multiple beneficiaries receiving a percentage of the residuary estate, or when the executor goes to court to file for an insolvent estate, or when there is a dispute amongst heirs. Without it, the court and/or beneficiaries have no way of determining whether the executor did something inappropriate.