Are you new to your job -- is that the reason for the concern?
When I first started my current, I used to worry about my amount of online activity. Then I realized that my supervisors, and their supervisors, are much too busy to worry about my time online, especially since I still got my work and tasks done.
That being said, don't abuse the privilege. If you can justify the use, that makes sense. If you're spending hours viewing/downloading content that really has nothing to do with your job, then you have something to worry about.