It refers to something that’s beneath one’s dignity. We hear and read this originally British term much less than we once did; it’s more often encountered elsewhere. That’s largely because in the UK it has become a cliché, linked to historical class attitudes that are commonly derided. The result is that it’s difficult to employ it other than facetiously. Sometimes, an attempt at humour leads to its appearing in a weaker sense of a thing that’s merely unfashionable:
Where rosé used to be infra dig, it’s now de rigueur.
Daily Telegraph, 13 May 2009.
It belongs to an earlier age, in which some actions or activities were beneath one’s dignity or demeaning to one’s station in life, a view taken seriously by the middle classes in particular. Commerce was the classic example; to be thought “in trade” would once have been mortifying. To undertake anything artisanal other than as a hobby was also inconceivable.
[Charles Darwin] was taught to see the oppressed black as a “brother”. This explains why, when he went to Edinburgh University at 16, he could apprentice himself to a freed Guyanese slave to learn the art of bird preservation without thinking it infra dig.
The Times, 22 Jan. 2009. The former slave was named John Edmonstone.
Infra dig is a colloquial Latin abbreviation of the phrase infra dignitatem, beneath (one’s) dignity. One example shows that a snobbish antipathy has not always been solely the preserve of the British:
It would be regarded as infra dig., I am told, for an American professor of English to concern himself too actively with the English spoken by nearly a hundred millions of his countrymen. He may, if he will, devote a lifetime to the English dialect of Norfolk or Dorset, but he may not waste his time and his dignity upon the dialect of his janitor, his barber and his trousers-presser.
The American Language, by H.L. Mencken, 1921.