You should get an RSS feed the next time you open MapInfo Pro stating that v16.0.3 is available to download and a link. If you missed that, then the easiest way is to go to the Pro tab to get to the backstage area and click on the Updates button.
The patch has quite a few bug fixes that should give you some better performance. And a couple of extra files if you need GDA datum support (Australia).
Don't forget to right-click on the update exe file and Run As Administrator.