If you Belong to a faction you may be given certain tasks that can be completed at game. Some may have a time limit while others will need to be done over several games.
Usually you will get a reward for doing these tasks and will result in positive Faction points in that group, while it may also result in loss of another faction points.
How you complete these tasks will often change the outcome of the tasks. Over all, the completion of a task will Further the group your in, resulting in more tasks for you to do, and changing the world. Also if you fail in a task the results could have dire consequences for the group.