The Maccabees and their followers decided to purify the Temple and hold the closest feast in their calendar. Sukkot, the Feast of Tabernacles. It usually takes place in October (the Bible uses a lunar based calendar), and celebrates the Fall harvest.. The Temple also needed to be purified and re-dedicated after the idolatry and sacrifice of an unclean animal. The purification process took eight days. The legend says that they only had enough oil for the lamps for one day and it would take eight days to prepare new oil. The lamps were lit anyway and supposedly stayed lit for eight days when the oil was prepared.
In both the books of the Maccabees and in the accounts of Josephus, the miracle of the oil is not mentioned. However, the Feast of Tabernacles lasted eight days and was also known as the Feast of Lights during that time according to Jewish sources.
The celebration of the eight day feast in the month of Kislev became known as Hannukah "Dedication" because Biblical Hebrew did not have a word for the more accurate "re-dedication." Although it is normally thought of a Jewish holiday, the only time it is mentioned in Scripture is in the Gospel of John.
Fast forward to the Puritans.
The Puritans wanted to rid themselves of all Catholic influences which they considered pagan, including Christmas. They even enacted laws banning Christmas and only celebrated holidays mentioned in the Bible. Modern scholars believe that the first Thanksgiving was actually the Feast of Tabernacles. Like the Maccabees, the Puritans wanted to purify themselves of non-Biblical influences and celebrated their delayed Feast of Tabernacles. Or perhaps, because the Geneva Bible used by the Puritans contained the Books of the Maccabees, maybe the first Thanksgiving was really Hannukah.