The Visibility Score is a score calculated by MobileAction to show how visible your app is in the market.
To increase your Visibility Score:
You will need to rank for a good number of keywords in decent rankings.
Find the best possible keywords for your app. These keywords should have both a high Search Score and a high Chance Score.
Aim to increase your average review ratings.
After accomplishing these 3 simple steps you will see an increase in your visibility score - the rest will be determined by the number of downloads you will get.
Good luck!