Local committee persons represent the smallest voting district of the state. In New York and New Jersey, it is a single "election district." In other states, it may be a precinct, ward or township. These districts are defined by population and generally consist of 700-1,000 registered voters. In an urban area, an election district may cover just a few city blocks.
A local committee person is elected to represent all the members of his or her party that exist within the election district. In principle, a committee person should be the most accessible and nearby elected official for community residents. Depending on the state and county in which you live, there may be two or more local committee persons from each party within your election district.
Note: Although you might assume that a committee person would represent the actual election district in which they live, according to New York election law, a committee person is only required to live within the same county and assembly district as the election district they represent.