This post is typed verbatim from Keys to the Japanese Heart + Soul, an excerpt from Japan: An Illustrated Encyclopedia.
(To persist, to hang on, to do one's best). An important word in Japanese interpersonal relationships. Probably derived from ga o haru (to be self-willed), the word originally had the negative connotation of asserting oneself against group decisions and norms. Since the 1930's, however, gambaru has become a positive word, commonly used to exhort enthusiasm and hard work, usually toward a group objective. For example, when a village youth leaves for a new job in the city, he promises his friends, parents, and teachers that he will gambaru. The implication is that he will try not to disappoint them. The word is also used among members of a group to encourage each other in cooperative activities, often in the imperative form gambare.
(BebeTaian's note: 'gambare' is also the term 'Ganbatte!' that you will hear frequently. It's kind of like "good luck!" here in America.)
Previously: Ojigi, A Followup