As with most American political ideas, Town Hall meetings have their roots in colonial America. These meetings were especially important in the development of democracy because it emphasized problem-solving through group efforts. It was even later called by Thomas Jefferson the "wisest invention ever devised by the wit of man for the perfect exercise of self-government".
By the late 17 Century, Puritan colonies were well established and the concept of family and village was of the utmost importance-- even living by yourself was prohibited. This was extremely different than any of the other colonies, such as the colonists at Chesapeake Bay, who only had interests in farming to gain wealth. Village members met together at meeting houses "Lord's houses" twice a week to practice what they had left England for-- religion. Even the distribution of land was dependent on the collaboration of villagers: the amount given was only enough to sustain the family, and those who were fortunate were expected to share what they had.
In any case, throughout many aspects of daily life, these Puritan colonies were tightly interlocked communities with strong obligations towards "group efforts". This, and the desire to move away from the highly centralized power of Church and state felt in England, caused Puritan communities to have local exercise of authority.
Once a year, all members of the village gathered to meet. Citizens elected officers to hold positions, and debated every and all issues concerning the village. Minor officeholders (town criers, measurers of salt, purchasers of grain) were elected in these town hall meetings which gave rise to the tradition of local government.