At first, I barely used them at all because I couldn't remember the rule and my players forgot they had them. Then I bought the
d20 Coins from Campaign Coins so I would have a physical representation for my F2F games and noticed the Star on the Portrait on Fantasy Grounds.
Now I use them all the time.
I use a variant/house rule (?) that a character can bank up to 3 Inspiration. This is mostly because I bought d20 Coins come in copper, silver, gold and Fantasy Grounds allows in the options to set the game to have up to 3 inspiration per player which shows up as up to 3 stars on their portrait.
However, I just tend to hand them out to players for great ideas and for just making the play experience better for everyone involved: a good joke, excellent plan, engaging roleplaying, etc.