To flourish is to grow vigourously, thrive, prosper or be successful. These grape hyacinths have really flourished since I first planted them.
Flourishing something is to brandish it or wave it vigourously, or to show it ostentaisiously. An elaborate expression, rhetorical embelishement or ornamentally curved handwriting could all be considered to add a flourish to your writing. (But not necessarily, especially those first two)
A fanfare played on brass is sometimes known as a flourish, as is an improvised addition at the end of a musical composition.
I hope you're well, in top form and a real flourisher!