I suspect that the question you're asking is really related to a body known as the House of Burgesses, especially if you're taking a history course. Town meetings, in themselves, were fairly common in isolated communities and not really worthy of class discussion. The fact that you mention Jamestown, though, is the tell-tale bit. I'll explain why:
Jamestown Colony was originally created as a money making venture. The Virginia Company sent out colonists to generate profit by cutting and growing and mining and whatever, and these colonists ended up at a place they named Jamestown (though it might have been James Fort originally, I can't recall.)
Anyhow, the company realized that men will work a lot harder for themselves than they will for a company, so it allowed settlers to actually own pieces of the land they were working and living on. Like any civilized Joes on their own acreage, these individuals became a real community that had a community's need for order and organization. The company responded with what were essentially town meetings to discuss local issues. It took too long for questions to travel across the Atlantic, be heard in England, and have answers sent back, so it was thought that some local form of authority would be far more effective for Jamestown.
The result, first having met in a Jamestown church, would eventually transform from a system of town meetings into what we know as the House of Burgesses (a Burgess is like a representative.) The reason this is important to US history is that the House of Burgessess was the first elected representative body in the colonies. It was a long taproot for democracy that would lead us to the government we have today.