The arsehole or arse-hole is of course simply a synonymn for the anus.
The Oxford English Dictionary states the word is "chiefly coarse slang", although this was not always the case. The first recorded use of the word appears in a manuscript in the possession of Gloucester Cathedral which is dated to the year 1379, although it is very likely much older, since the word arse itself dates back at least to the end of the first millenium. Indeed both arse and arsehole are simply examples of a good old solid Old English words, which like many such words subsequently came to be regarded by the Frenchified upper classes as rather common.
In its modern 'slang' usage the word arsehole is generally used to refer to either a particular geographic location regarded as possessing certain undesirable qualities, or to an individual sharing much the same characteristics. Geographically speaking, the first place to be granted the honour of being "the one true and original arse-hole of creation" was Los Angeles, California, as designated by Henry Louis Mencken in 1926. Which, if nothing else, at least shows that the adoption of the more 'polite' variations of 'ass' and 'asshole' by the American colonials is a comparatively recent linguistic development. The use of the word to describe a "stupid, irritating, or despicable person" appears to be more recent, as the earliest example the Oxford English Dictionary can track down is that of Roger Scruton who described one character as being "an arse-hole of the first order" in his novel Fortnight's Anger which was published in 1981.
SOURCES
Sourced from the Oxford English Dictionary and personal knowledge.