A 'pair-royal' is three cards of the same kind - three aces being better than three Kings etc.

'Braggers' are, in effect, wild cards, sometimes specified as the Knave of clubs and the nine of diamonds, or simply Knaves and nines of any suit. A pair-royal of kings can be made with two kings and a bragger, or sometimes one king and two braggers.

The Austen family seem to have been playing a variant in which three braggers (nines or Knaves) can make a pair-royal.

There seem to be many variants of the rules regarding braggers, some of which are given in online editions of 'Hoyle's Games', which was a compendium of rules for card games etc, first published in the 18th century, and in many later editions.
Braggers are also mentioned in the Rules of Brag posted by Myretta, near the bottom of the page in a section headed 'Variations'. The last paragraph states that there is no evidence that Brag has ever been played using three wild-cards or Braggers, but JA's letter 64 appears to prove that it was.