My two daughters demanded to know this. I speculated that it was artificially inserted, perhaps in the 17th-18th century, perhaps to make the word look more like populus, somewhat similar to the way the spurious ‘s’ was added to ‘island’. I later learned that the Middle English spelling was peeple or peple, which I think tends to support this hypothesis, but I don't know. The picture is further confused by the existence of the Old French form people. Perhaps the ‘o’ was dropped, and then the older form was revived?
I consulted several dictionaries before posting this, including the Online Etymology Dictionary, and did not find any with a definitive answer.
Is anything specific known about the introduction of the ‘o’?