Green vaginal discharge with itching of the vagina is not a good thing and is a sign of either a bacterial infection or a sexually transmitted infection.
Either way you have some sort of vaginal infection that needs checked out by a doctor to find out exactly what kind of infection you do have.
You could have the sexually transmitted infection known as trichomoniasis which is a common STD or sexually transmitted disease that is caused by an infection with a protozoan parasite called Trichomonas vaginalis.
If you haven't been sexually active or had sex with someone then it's likely just a yeast infection or other vaginal infection.
It still should be checked out if you're having green discharge from your vagina because it's not normal and is a sign that something is wrong.