Many Army enlisted jobs and assignments require a security clearance. In order to obtain a security clearance, one must be a U.S. Citizen. You can still enlist without U.S. Citizenship, but your job choices and assignments will be limited to those which do not require a clearance.
Of course nobody can tell for 100 percent certain whether or not a security clearance will be approved, and the process can take several months. This is where the Security Inteviewer comes in. He/she will ask you a whole bunch of questions about your past (drug use, alcohol use, mental health treatment, finances, criminal history, etc.), and is pretty good at making a prediction as to whether or not you're a good candidate for security clearance approval. This, in turn will affect which Army enlisted jobs you are eligible for.