Veep is a casual, slightly playful word for a vice-president. It is used both for the vice-president of a country — in American news and jokes, especially — and for a vice-president inside a company, of which a big American firm may have dozens. The tone is the whole point: 'vice-president' is formal and a bit heavy, and 'veep' is what you say when you want to sound light, quick, or a little cheeky about the job. It carries a faint hint that the position sounds grander than it is, which is exactly why a well-known American comedy series about a vice-president was called Veep. It is chiefly American, informal, and you should not put it in a formal letter or a news report — reporters write 'Vice President Smith', not 'Veep Smith', unless they are being funny on purpose.