A Public Task is a task that has players work together to reach a common goal. A Public task can be completed with just one person, but the difficulty is designed for several players, so it will take longer and may be more difficult. Public Tasks can be repeated as many times as you want, and you are free to leave whenver, though you will lose participation credit for the quest.
The reward for a public task is based on rank. While each player is working towards the same goal, the player who does the most work will be ranked at 1, while the player who did the least will get a rank equal to the number of players in the quest. Xp and Clams very based the higher your rank is. At the end of the quest you will also receive the option to pick a prize for completion of the quest. A player with a rank of 1 will recieve more options to choose from than a player ranked at 5. Generally the lower rnaks will get to pick from items for collection, but a higher ranked player will also be able to pick clothing items unique to the quest.