Dual citizenship is recognized by the US under limited circumstances. If you are a citizen of another country & the US at the moment of your birth the US recognizes it.
If you are a dual citizen, once you are no longer a minor if you do not renounce your non-US citizenship there will be limitations primarily having to do with government employment, obtaining a security clearance, obtaining a private sector job that is wholly or partially supported by government funds. Note that joining the military is still possible, though your available jobs will be limited, and you are still subject to the any draft.