I know this, but I can't recollect at all.
What is this thing called?
They are usually centered in a book or writing and I'm certain they have a name but I can't remember for the life of me. They also come in all shapes, colors and sizes.
Flourish, Filigree, or Ornament are common terms.
Usage doesn't generally change the name. Simply because it's been used by the book designer to separate content, there's no special term I'm aware of for that specific type of usage.
There are some fleurons available in the Unicode specification under the Dingbats block (PDF).
- 273E ✾ SIX PETALLED BLACK AND WHITE FLORETTE
- 273F ✿ BLACK FLORETTE
- 2740 ❀ WHITE FLORETTE
- → 1F3F5 🏵 rosette
- → 1F4AE 💮 white flower
- 2741 ❁ EIGHT PETALLED OUTLINED BLACK FLORETTE
- → 1F3F6 🏶 black rosette
- 2766 ❦ FLORAL HEART
- = Aldus leaf
- 2767 ❧ ROTATED FLORAL HEART BULLET
- = hedera, ivy leaf
- → 2619 ☙ reversed rotated floral heart bullet
- → 1F65B 🙛 south east pointing vine leaf
Many of the other Wingdings fleurons were recently added to the Unicode specification under the Ornamental Dingbats (PDF) block.
Fleurons are leaf or floral-shaped ornaments used for text decoration.
Screenshot of text because most of those glyphs are not yet supported (in my browser anyway)