Pro forma means "for form" or "for form's sake" and is from the Latin. For financial statements, it is an "as-if" situation.
There are times when a company wants to or needs to present its financial statements in a presentation that differs from Generally Accepted Accounting Principles (GAAP). When it does so, those statements are called "pro forma."
For instance, a company has just purchased a competitor which has increased earnings quite a lot. On a pro forma basis, the earnings of the original, underlying company can be viewed, as if the purchase had not occurred, for such things as comparison purposes to a previous period. Other examples include what would conditions would be if a proposed debt issuance is finished or if certain expenses are not included.
Companies usually state that the pro forma version is a more accurate representation of the actual performance of the company. This may or may not be true. If the company has just finished an acquisition, then it can be very helpful to see what it would have been if that had not happened, assuming all else had remained equal. But if the company is excluding certain expenses, such as stock-based compensation, to show that it would have earned more money if those expenses were ignored, then the company is probably spinning its results to make them more favorable to investors.