Great question! As an aerospace engineer, you will have several different options of career paths. The most obvious will be to work in the aerospace industry largely on government and private contract work. For example, this could mean working for a large aerospace company or the government working to build and test airplanes, jets, radar systems, missiles, etc. A second option will be to work for a consulting firm where you help advise aerospace clients on whatever challenge they may be facing. A career in consulting will offer a lot of variety of clients and the challenges you will face but will likely be less engineering technical and more big-picture than if you worked in the industry.
I recommend that when you attend college, talk with your advisor and career services about additional opportunities for aerospace majors. They are great resources and will have more specifics on who specifically recruits from your university or campus.
Best of luck!