Ballpoint pens, as the name suggests, [have a ball on its tip](https://i0.wp.com/ipwatchdog.com/images/writing-instrument.jpg) which makes contact with paper, displacing ink from it in the process. When a pen is not in use for a while, the ink on the exposed side of the ball dries out and gunks up the tip, blocking new ink from flowing out. Rolling the ball vigorously tends to break off the gunk and get the ink to flow again.
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