Daven is the Yiddish word for "pray," which has passed into common Jewish usage. But it doesn't quite have the same connotations as the English word.
Prayer is likely to conjure up images of neat, kneeling rows of worshippers, with hands pressed together and eyes turned piously heavenwards. Daven is more likely to evoke pictures of crowded, slightly chaotic shtiebls, and shockelling worshippers engaged in impassioned conversation, supplication or song. The word is redolent with the informality of the Yiddish-speaking world and its at-homeness with the divine. Like many of the best known Yiddish words, the origin of daven is obscure. (Lobbes is another example - does anyone have a clue where that comes from?)
I know of two theories on etymology of daven. The first is that it is a medieval borrowing and corruption of the Latin "divinus," which means "divine," or "divinar," "to prophesy." The second theory, which I have heard attributed to the American Jewish studies professor Arthur Green, is a little more involved. Apparently the word daven means "gift" in Lithuanian.
When Jews trading in the marketplaces of Lithuania would break off their work in order to daven Minchah, the afternoon service, they would explain what they were doing by translating the word Minchah, which means "offering" or "gift," into the vernacular.