Does it mean she has STD when her vagina mells bad? How can we cure it and can I also be infected because of my gf's bad smell down there?

Not necessarily. Vaginal odor is not necessarily due to an std. It could be due to bacterial vaginosis, which is an overgrowth of certain bacteria that is not classified as an std. If it is an std, you could catch it; if not, than you couldn't catch it. Either way, it would be worth a trip to the ob/gyn to determine what the cause of the odor is.