The term is supposed to have been originated by Cardinal Newman, when he was confronted by the argument that, as a Catholic priest, he did not place the highest value on the truth. The allegation was that since Cardinal Newman was personally biased towards the Catholic position, he could not be relied upon a source of fair or impartial argument.
This is a somewhat oddly understated way of putting it. Kingsley's accusation in the dispute was not that Newman was biased because he was Catholic; it was that Newman was dishonest because he was Catholic. As he put it,
I am henceforth in doubt and fear, as much as any honest man can be, concerning every word Dr. Newman may write. How can I tell that I shall not be the dupe of some cunning equivocation, of one of the three kinds laid down as permissible by the blessed Alfonso da Liguori and his pupils, even when confirmed by an oath, because 'then we do not deceive our neighbour, but allow him to deceive himself?'
To this, Newman replied,
But what shall I say of the upshot of all this talk of my economies and equivocations and the like? What is the precise work which it is directed to effect? I am at war with him; but there is such a thing as legitimate warfare: war has its laws; there are things which may fairly be done, and things which may not be done. I say it with shame and with stern sorrow;—he has attempted a great transgression; he has attempted (as I may call it) to poison the wells....[W]hat I insist upon here, now that I am bringing this portion of my discussion to a close, is this unmanly attempt of his, in his concluding pages, to cut the ground from under my feet;—to poison by anticipation the public mind against me, John Henry Newman, and to infuse into the imaginations of my readers, suspicion and mistrust of every thing that I may say in reply to him. This I call poisoning the wells.
The claim that the tactic is 'unmanly', incidentally, is a swipe at Kingsley, who was famous as a member of the Muscular Christianity movement, devoted to the ideal of Christian manliness, and who often swiped at Catholic priests for being unmanly and feminine due to their celibacy and dishonesty.
In any case, the dispute, of course, was the occasion for and subject of Newman's autobiography, Apologia Pro Vita Sua, which is explicitly written to clear himself of any charge of untruthfulness on the subjects with which he had been arguing with Kingsley.