Someone who is unambitious isn't particularly motivated to achieve some kind of success. Do you prefer lying on the couch to doing extra credit? When it comes to school, you're unambitious.
An ambitious person has an obvious interest in succeeding at something. If you're determined to climb Mt. Everest, and you train hard in preparation, you're ambitious. If you're not particularly motivated about that or anything else, you're unambitious. Ambitious comes from the Latin ambitiosus, "eager for public office" or "eager for favor." Add the prefix un-, meaning "not," and you get unambitious.