I agree with @Jay about the meaning (and would expand it to say it explains the difference between revenue and profit), but to provide a little more context, someone did some research into the history of this joke and found that it was
from a newspaper (the Saturday Review) from 1876.
Cite: 1876 November 11, The Saturday Review, Mr. Froude on Landed
Gentry. Page 592, Column 1, John W. Parker and Son, Published at the
Office of the Saturday Review, London. Google Books
If this is a state of things which he approves it is difficult to
understand his reason for introducing an account of the doings of the
late Mr. Augustus Smith in the Scilly Islands. The natives of that
group, before Mr. Smith's time, are popularly said to have eked out a
precarious livelihood by taking in each other's washing. Now things
are very different, and the people are well fed, well lodged, and well
The person doing the research Garson O'Toole found that a later reference from 1885 that "mentioned three popular American writers:
Josh Billings, Artemas Ward, and Mark Twain" but did not specificly credit any of them with the authorship.
Cite: 1885 December 5, The Critic, The American Humorists,
[Acknowledgement to London Daily News], Page 274, Column 1, The Critic
Company, New York. Google Books
In American country newspapers there is usually one column entirely
devoted to facetiae, which appear to have been clipped out of the
columns of other country papers. They live on each other, just as the
natives of the Scilly Islands are feigned to eke out a precarious
livelihood by taking in each other's washing.
Garson O'Toole's email suggested that there was a 1866 variant involving the Isle of Man, but I wasn't able to find the cite he was referring to (possibly that was a typo of the 1876 cite, but that wasn't involving the Isle of Man).