Revenue is the amount of money a company is allowed to recognize from the sale of its goods, services, or intellectual property during an accounting period. It is synonymous with "sales", turnover or "top line."
You might think that revenue = sales, so the number you see on the income statement is exactly how much money the company brought in from selling its stuff. Yes and no.
Yes, because that is how a company generates sales, by selling its "stuff" be it goods, services, or intellectual property. And the company gets paid for that.
No, because of a couple of things. First, the number shown on the income statement is usually "net" of various items, such as expected returns. Having tracked sales, delivery, and returns, a company knows how much of the stuff it delivers will be returned on average, so it nets out this amount, showing how much actually remains in the customers' hands.
Second, thanks to accrual basis accounting, the company usually hasn't received all the cash it is owed for the stuff it has sold. Very often, the company will issue short term credit, delivering the goods or services before payment is received. However, if the company is reasonably sure that payment will indeed be received, the company is allowed to "recognize" that sale as revenue.
How and when a company "recognizes" revenue is very important, as it determines how much net income a company will show in any given accounting period. For instance, if a company cannot recognize revenue until 100% of the item is delivered, but it has to show expenses as they happen, then net income is going to be depressed until all of a sudden, when it "earns" that revenue, net income will shoot up to a high level. Now, usually, a company in this type of situation has several projects going on and is recognizing revenue from older projects, so things won't be quite that lumpy (net loss, net loss, net gain, net loss net loss, net loss, net gain, ...), but you can see how this type of revenue recognition would affect the "worth" of the company if all you did was look at the net income line and saw losses and gains coming in at seeming random intervals.
Further, if a customer does not or cannot pay for what it bought, the company can no longer recognize that revenue as "earned" because the reasonable expectation of payment no longer holds.
How a company recognizes revenue is usually one of the first footnotes found below the financial statements and should be read assiduously so that you understand how a company makes money.
Revenue vs. cash
Because revenue can be recognized before the customer pays for what was sold, revenue does not equal the amount of cash brought into the company during the accounting period. Some of what has been sold has actually been paid for, so that results in cash. But some of what has been sold hasn't been paid for yet. In this case, then the accounts receivable account on the balance sheet is increased by the amount that has been recognized but not paid for yet.
However, the company is also collecting on older receivables, so the balance of that account is going up and down as sales are made and cash is collected. It's not a linear relationship, in other words.
Tying into the income statement
Net revenue is listed at the top of the income statement and is thus often called the "top line." All the expenses used to generate that revenue during that reported time period are then listed below it and subtracted from it. The end result is net income at the bottom of the income statement, called, unimaginatively, the "bottom line."
Revenue is only reported for ongoing operations. If a company is selling or has sold a division of itself, the sales generated by that division are not included in the top line. Instead, that will show up lower down the income statement, as part of "discontinued operations," usually just above net income (after tax owed or due has been shown).
Other types of non-revenue gains are shown after the operating portion of the income statement, such as gain on sale of assets or investments, or one-time gains such as from the payment of a lawsuit settlement. Don't confuse these with "revenue."