Accruals accounting is a method of accounting that records revenues and expenses at the time that a transaction occurs, regardless of when cash actually changes hands. Most companies operate under an accrual system.
A key reason for differences between an accrual accounting system and a cash-flow based one is buying on credit, or any other form of deferred payment. If a company closes a sale, but the customer doesn't pay for 60 days (after receiving a bill, etc) an accrual system would immediately recognize the sale, on the theory that the company is highly likely to be paid, while a cash-flow based accounting system wouldn't recognize the revenue until money actually changed hands.
An accrual system can more accurately depict a company's financial situation by recording revenues and expenses in a more timely manner. However, any accrual system is subject to management judgment - about when to accrue (ie, when a sale is considered "certain") and about the likelihood the company will eventually be paid for its services. However, there are accepted accounting standards for when to accrue and what assumptions can be made around bad debt for accounts receivable.