It means you have saved analysis.
What does a star on Analysis button mean?

How do you view a saved analysis?
If you're asking about the analysis the OP was talking about, you use that button on a daily game that has saved analysis.
If instead you mean sabers ones from completed games or an Analysis Board then https://www.chess.com/analysis/saved
That link can be found in previously Analyzed games.
Hello. Sometimes I see a star icon on Analysis button. What does it mean?