I often get it after hard fights like gyms and bosses.
Its in the bottom left corner, and is simply a pikachu wagging a joycon from side to side.
I'm guessing it is a reminder that the 2 player mode exists? I'm using the red joycon and he has the blue one.
But I never got a tutorial or an in game explanation of what is that icon.
EDIT: Also, there's the constant reminder of the 2 player mode with the green icon, that is usually bottom right.