Your passport allows you to travel outside of your country, as well as return home again. Please keep your passport in a safe place, and do NOT carry your passport with you in the US. IES recommends carrying a photocopy of your passport with you.
Your passport should never be allowed to expire. When your passport is within 6 months of expiring, you can work with your country’s Embassy in the US to apply for a new passport, typically through your Embassy’s website. If you renew your passport, but your visa stamp is in the old passport, you can carry both passports with you until the visa stamp expires and you get a new visa in the new passport.