Simpson, Jacqueline and Steve Roud, A Dictionary of English Folklore (Oxford: Oxford University Press, 2000) is always a good source for this sort of thing. 'Jack o' Lantern (aka Jack-a-Lantern) is the name of a supernatural being 'mainly in East Anglia and in south-west England' but also it is a name for a carved turnip - which appears in North American as a carved pumpkin. The supernatural being is also known as a 'Will-o'-the-Wisp' notorious for its phantom light that easily misdirects travellers. The Cornish rhyme recorded by Thomas Quiller-Couch in his book on Polperro, Cornwall (1871), includes the following (after Simpson/Roud, p. 197):

Jack o' Lantern! Joan the wad, Who tickled the maid and made her mad! Light me home, the weather's bad.

Simpson and Roud maintain that the idea of carving turnips or swedes with faces, lit from the inside with candles, was a traditional means in England to scare people on All Hallows Eve (i.e. Halloween). This practice is echoed by 'Punkie Night' when similar carvings were used in Somerset on the last Thursday in October to light the way when going house to house to ask for money.

This site recalls a legend that is often referred to as the source of the Jack o' Lantern custom; namely the spirit of a man who wanders the earth carrying with him a bit of burning coals that he has taken from Hell. He is unwanted there as well as in Heaven, so he is forced to walk the earth with his unearthly flickering flame. This legend is more likely to have been attached to the practice rather than causing it. It is equally important to note that the website does not refer to the core of your question, specifically as to when the practice originated - even though the site purports to be a 'history' site. So it goes too often with folklore: it's easy to find early references to the practice and even to determine where it is likely to have originated, but the 'when' of its origin is typically difficult to discuss. The practice merely emerges, full grown, into the historical record, with little clue as to when it actually originated.

The Wikipedia article affords us an opportunity to 'take the temperature' of contemporary folk belief regarding the origin of the practice. It is necessarily - and accurately - vague about the origin. Attempts to pin it on the Irish is dubious since it appears full-grown among the folk of Britain at the same time. It is more likely that it was widespread for a long time and simply shared between Britain and Ireland, from which - in equal parts - it diffused to North America. And it is in North American that people began to employ that much better resource of the pumpkin - I can't even imagine attempting to carve a turnip after having the ease of a pumpkin at one's disposal!

So this answers some of your question, namely the likely where. The why is that it was likely inspired by the phantom lights often associated with marshes and ascribed to supernatural beings - inspiring mischief makers to replicate the 'look' for pranks associated with Samhain/Halloween and or autumn celebrations in general. The when - we can comfortably say ' a long time ago', at which point I will retreat into my folklorist's easy chair and regard this answer complete (with an appropriately vague answer)!