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.
Bacterial vaginosis? The main cause of strong vaginal odor (often fishy and strongest after sex) is bacterial vaginosis, an overgrowth of mostly normal bacteria. BV itself does not affect men. However, the STD trichomonas causes the same odor, and STDs like gonorrhea and chlamydia are more common in women with BV. She should discuss STD testing with her doctor, especially if either of you had other partners recently.