If you've signed up for Student aid and your paperwork states off campus housing that means that you would be living off campus and the student aid is likely gonna pay for your off campus housing.
Now if you're just signing the forms then off campus means that you plan to live off campus and want to get student aid to pay for off campus housing.
On campus would mean that you plan to live on campus which means that you plan to live on the grounds in a dorm room on the college grounds.
Some people will qualify for off campus housing help while others may not.
Also be aware that for the first year at least you may be required to live on campus but then can move off campus after the first year if the college requires that you live on campus the first year.