A man's private parts is the penis or also called the balls. It is the part he uses to get a girl pregnant in sex. He will insert the penis in a girls private which is called the vagina. They also call this, sexual intercourse. This is how your parents had you/made you.
The woman's private area is collectively called the vulva. The part at the lower end of the vulva where a man inserts his penis is called the vagina. The vagina is also what is commonly called the birth canal.
There is public and private. Private is when you are by yourself or with a limited amount of people. An area could be called public because you would be around hundreds of people. Examples of public places are a restaurant, school, camp, and fairs or carnivals.