Credit cards

What does it mean when you make someone an authorized user on your card? Do they build their own credit or does your credit become there’s? Does their card activity affect yours and your credit?

My daughter is wanting to move out but keeps getting rejected because she doesn’t have credit, she has never had a credit card. I’m trying to help her somehow. She’s pregnant and her and the boyfriend want to live together but neither have credit. Yes she works full time. She applied for a credit card at 3 banks (BoA, Capital One and Chase) and they all denied her because “income is insufficient”. I saw the email myself. It makes no sense. I can’t co-sign because my income isn’t enough, I just have good credit. She has good income (40k) and no credit.