Can I apply for social security at the age of twenty? What exactly is social security for?

You can apply for social security. Social security is actually a kind of public insurance. If you are a 20-year-old student, you should apply in the school. If you are a social worker, you can apply for it yourself. If you succeed, you will be sent a social security card. Generally, you can reimburse medical expenses by swiping your card directly when you see a doctor.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.