Board Thread:General Discussion/@comment-23.126.55.222-20170228004048/@comment-30514476-20170228011000

The visit counter is the number of visits for which you can receive the bonus reward for visiting. This bonus reward is extra experience points, coins, and access passes to the premium locations.

The number begins at 5 for new players and increases as your reputation level increases. And it will be capped at 100. So the number depens on your own reputation level (which you can increase by visiting your friends and clicking on their maps to charge their trophies & locations). And not the number of times friends have visited you.