Their family has many descendants (is thriving with offspring).
Tips
culture
兴旺发达 (xīngwàng fādá) is a common New Year blessing meaning 'prosperous and flourishing'. 人丁兴旺 (réndīng xīngwàng) means having many children/descendants.
usage
兴旺 often describes businesses, families, or communities. 繁荣 (fánróng) is more formal and used for economies/nations.
