To vie for something means to compete for it. Two teams may vie for the gold medal, but one will have to go home with silver.
Vie may be spelled the same as the French word, vie, but they are pronounced differently, vī and vē respectively, and are not related in meaning or history. English vie comes from the Latin verb meaning "to invite" as in to invite a challenge. Be careful of the spelling which includes an ie to y shift. “He intends to vie for the top prize,” but “He is vying for the top prize.”