EBITDA is Earnings Before Interest, Taxes, Depreciation, and Amortization.
Because D&A can be quite large, adding this back in will often convert a negative operating profit (and, by extension, a negative net income) into a positive number, which is considered "better" by investors and analysts. "Hey, look! If you ignore a bunch of the rules of generally accepted accounting principles, we made money!" Because of this type of spin, Charlie Munger has said, "Every time you see EBITDA earnings, you should substitute '[censored] earnings'."
EBITDA first came to prominence in the 1980s during the period of a lot of leveraged buyouts. Investors wanted a quick metric to see if the company could handle the increased interest payment load in the short term that the restructuring would lead to. Since then, it has expanded and is used by many analysts and companies. Proponents say that it shows how a company is behaving on an operational level by stripping out expenses that might otherwise obscure things. However, depreciation and amortization are real expenses, being the "expensing" of assets purchased via capital expenditures over the lifetime of those assets. D&A, to abbreviate them, are legitimate expenses.
It is also useful for comparing companies of different capital structures (though EBIT would work as well for just that), tax rates, and depreciation policies. Investors and analysts, however, can usually adjust for such differences, at least the latter two.
One thing that keeps it popular, though, is that it shows a larger number than net income or operating profit would, thus making the company appear to be more profitable than it may truly be.
Using EBITDA can overstate the company's interest coverage ability. For instance, if it has $12 million in operating profit, but $14 million in interest payments, things look a lot better if you can add back in $8 million in D&A expenses, so that it shows $20 million to cover the $14 million in interest.
Using EBITDA also is not a substitute for cash flow, as it ignores changes in working capital. By ignoring important business expenses, it can overstate the apparent cash flow.
Finally, it can make the company look cheaper than it really is. If one uses a price multiple to EBITDA. A 7 multiple sounds a lot better than a 20 multiple does.