When a baby is born, she comes into the world through birth. If you say, "I was born in July," that's the month in which your mother gave birth to you.
You can talk about a newly born baby or ask your friend what year she was born. Even ideas or organizations can be described this way: "My book group was born in 2005." If you're a really good bowler, you can also say you were born to do it, or that you're a "born bowling champion." The Old English root of born is boren, the past participle of beran, "to bring, bear, or produce."