In artificial insemination, all that's done 'artificial
ly' is the introduction of the semen
into the prospective mother
by, er, something other than a penis
The term, and the practice, I suppose, was first a big deal for cattle in the second half of the 20th Century, when the man from the Ministry (of Agriculture) would go round the farms with a load of bull's semen and impregnate all the cows. The artificial insemination, or AI, man, was known to farmers as The Bull in the Bowler Hat.
In humans, AI is used whenever the woman in question doesn't want to have sex with the sperm donor, or the sperm donor doesn't want to have sex with her, but pregnancy is the desired result.