Branched means that you've been told which branch of your service (in our case, Army) you are going to be in, INF being one of them (INF/IN=Infantry, AR=Armor, FA=Field Artillery, etc.). Your rank on the OML (Order of Merit List) determines your priority for getting the branch you request (ROTC contracts say "for the good of the service" and the DoD can send you anywhere they feel is best for them, not you).
And I say ARRRR! because I put the ARRR in Army. Just kidding.