On a scale of 0 to 10, where 0 means perfectly acceptable and 10 means rude and completely inappropriate, this is about a 3 or a 4, about the same as the word "crap." If you search for the Wikipedia article "seven dirty words" you will see that "balls" is not among them. "Balls" can be slang for "testicles," and that's what it is here. (Other words that can mean testicles are "stones," "nuts," and "cojones.") The glands in the testicles, the testes, secrete steroids, which enhance aggressive behavior. It is often thought that this is the source of a man's virility, courage, daring, and bravery. "Balls" suggests just the right amount of recklessness and willingness to take risks. "I don't have the balls to do something" isn't a sexual statement. The slightly-taboo word "balls" is just being just to intensify the statement. There are two other phrases that mean just about the same thing, that are completely acceptable, and could be used by either a man or a woman: "I don't have the nerve to do [something]" and "I don't have the guts to do [something]."

It is very informal the first one.

Balls is slang for testicles. So it's saying that one is manly enough to do something, having the potency (/the courage) to do something. In addition it means that you have guts to do something hard. Be aware that is a very informal and impolite expression which is used just in funny and friendly situations with your close friends!

yes, it is informal. Most people we would only use such an expression with close friends and in informal situations... like hanging out with friends for family...... etc..... A little more polite with the same meaning, "I don't have the nerve to do something"

Only use the first phase with close friends. If you use it with people you are not friends with, it will get you in trouble.