The vagina is a part of a woman's body: the tube inside her that goes from the outside opening up to the uterus (the place where a baby grows). It is a real body part with a real name, and doctors, nurses, health books and school biology classes all use this word plainly. It is not a rude word, but it is a private word — in normal daily talk people do not say it unless there is a reason, like talking to a doctor, reading about health, or teaching a child the names of body parts. Say it calmly, the same way you would say 'stomach' or 'lung', and nobody will think anything of it.

One thing worth knowing: many English speakers use 'vagina' loosely to mean the whole outside area too. In careful medical English, the outside parts have their own name — 'vulva' — and 'vagina' means only the inside tube. So when you read a health article and it seems to say two different things, that is why: the everyday use is wider than the medical use. The adjective is 'vaginal'.