The main difference between these two forms of accounting goes right back to timing. Of course, timing has a partner here. It is called revenue recognition. Cash basis only records revenue when cash is received, and not a moment before. It also only recognizes an expense when cash has been paid out. So, even if a bill is sitting on your desk, if it has not been paid, it is not considered an expense in cash basis accounting - at least not until you write a check to pay that bill.
In the accrual basis, revenue is recognized when it is earned and not when it is received. Expenses are recognized when bills are received regardless of when they're paid.
Another pretty important difference in these two forms of accounting is how well cash is tracked. Cash-basis accounting does an excellent job of tracking cash flow because it records the inflows and outflows only when they occur. However, it does a horrible job of matching revenues and expenses in the accounting period that they occur.
Accrual basis does an excellent job of matching revenues and expenses and a poor job of tracking cash flow because it recognizes income before it is received and expenses before they're paid.
A third example of differences between these two types of accounting methods is this: in order for a company to use cash-basis accounting, it can't sell items using in-house charge accounts that would result in an account receivable. It must only accept cash, check or credit cards as payment. Under the accrual basis of accounting, the company does have accounts receivables.