Honestly, it will probably be easier when you watch the movie; you'll see Han presumably reach for a switch/lever, and the visible barrels will fire with that traditional cannon kickback.
The funny part about it is that it's kind of a throwaway moment, the firing on the TIE; and yet they specifically made a point to construct a cannon there. But it's seemingly never referenced (or shown) anywhere else in the movies, or in any technical literature that I can find on the Falcon.
EDIT: Holy crap, I think I'm totally wrong. I think the "motion" on the "guns" is the light shifting on a hanging silhouetted piece inside the cockpit, which would make the blasts from the TIE. So maybe he's reaching up to hit a switch to turn the alarm off?
For 30+ years I've interpreted that scene wrong, and now I've gone public with it!! My apologies to all!!