The characters are the citizens who live in Harvest Town. While the majority live in the center of town, many live in different places across the map. Each villager has a distinct schedule and preferences, and will provide you with a quest to complete from time to time. Many of them are also in charge of the various shops around town.
Single villagers are those romanceable and have 12 possible hearts instead of the usual 7 hearts, and are in the categories of Bachelorettes and Bachelors.
Special characters are those that appear in specific events and are not readily found around town.
See also the NPC Gifts Table for a quick overview.