Infra dig is slangish Latin for infra dignitatem, meaning "beneath one's dignity". The truncated form was coined sometime in the early 1800s, when it was used frequently in periodicals for cultured gentlemen, perhaps most frequently in The Monthly Mirror, a collection of essays focused on the theater. It was arguably popularized by Sir Walter Scott in his novel Redgauntlet (1824), and some sources credit him with coining the phrase in this book; this is untrue.
"It would be infra dig. in the Provost of this most flourishing and loyal town to associate with Redgauntlet."
Infra dig has remained in fairly common use among the literati, although its popularity waxes and wanes. Google Ngrams indicates that it was most popular between 1847 and 1946, with a peak in 1860. In 1929 it transitioned from being most often written with the full stop ("infra dig.") to mostly not. Since the 1980s its use has been in steady decline. It is still very much a "fun" way of using a comparatively uncommon Latin phrase, and as such is inherently limited in the contexts that it is appropriate to use.