In accounting, an expense is a general term for an outgoing payment made by a business or individual. Expense reports are records of those payments.
One specific use of the term in accounting is whether a particular expenditure is classified as an expense, which is reported immediately to the investing public in the business's income statement; or whether it is classified as a capital expenditure or an expenditure subject to depreciation, which is not. These latter types of expenditures are reported eventually, but not immediately, by business that use accrual-basis accounting, meaning all large businesses.
In investing, one controversy that mounted throughout 2002 and 2003 was whether companies should report the granting of stock options to employees as an expense on the income statement, or should not report this at all in the income statement, which is what had previously been the norm.