Demonstrated Interest" may be a factor a college of institution uses in determining whether or not an applicant has shown genuine interest in attending in their admissions review. Demonstrated interest can take the form of a campus visit, interview, other contact with the admissions office, even smaller tasks like signing up to request information on the college's website or opening emails sent from institutions. This assessment helps admissions officers to manage a critical statistic, yield, the percentage of admitted students who eventually enroll. Students who have shown some interest may be read more favorably than those who have not because they are seen as more likely to enroll if admitted.
All are strongly encouraged to read THIS ARTICLE, which does a great job of further highlighting this concept and the myriad ways in which interest may be tracked.
As you begin to identify colleges and universities to apply to, remember to connect with each of them in some fashion in the coming months. Don't go too far; showing interest is only one piece of the puzzle. Don't bombard admissions offices with unnecessary emails or phone calls, waste time with multiple campus visits, etc. Being annoying is never a helpful strategy. Simply make sure to show some interest in the colleges to which you think you’ll eventually apply, particularly those you might see as “safety schools”.