That shows the number of "nices" you have received. You may have experienced a series of stars and a cloud with "nice" written in it appear on the PSS screen. This means that you have just received a nice from another player. Nices are basically likes, to show you like that player or to say gg, etc.To give other players nices, you need to click their icon, then the "nice" button on the top right corner.
Hope I helped!
Source: Experience
Edit:
>Using the PSS, you'll have full access to your entire friend list, being able to see who is online and what they are doing in real-time. If you tap their icon, you will be given a variety of options. First, you can send them a "Nice" for their activities.
-Serebii
I can assure you that is what the icon does, and the star numbers represents the number of nices you received. I have done it countless times, and received nices in response. Also, it does say "nice" and a message even appears saying "you niced player"(to memory). It probably just takes time to register.
