What does it mean that larger banks are using the deposits of people moving from First Republic (FRC) to shore up First Republic?

Just saw the headline of what is happening today. Apparently people are moving their money from First Republic to larger banks, including many larger banks that are now using those deposits to help “shore up” First Republic to the tune of tens of billions now, and climbing. What does this all mean? Because it looks like a shell game to a lay person.