As of November 11, 2012, the PSUPedia and its affiliated wikis have made the transition to read-only mode. While edits can no longer be made, we hope you will continue to enjoy the data collected by the community for years to come!
From The PSUPedia
Story missions are special single-player missions which continue the story started in the offline mode of the original Phantasy Star Universe. These missions have unique differences that separate them from normal free missions. One of the largest differences is that if you are incapacitated at any point (even if you have a Scape Doll in your inventory), the mission will end in failure. Also, as stated before, story missions are single-player only, so you cannot invite other players or NPCs. Each story mission, or chapter, is divided into two acts, both of which have a trial in which you will be graded on your performance. Aside from the normal Meseta and MP rewards, if you obtain an S-rank while playing on difficulty level A, you will be awarded 10 PA Fragments. Keep in mind that the PA Fragment reward is only given out the first time you complete the trial with an S grade. Subsequent completions will give out only Meseta and MP.
Episode 3 introduces a new element to how story missions play out as you progress: repercussions of your choices. The choices you make as well as how well you perform during certain trials will activate new events in existing story missions, thus opening new subplots. Please see the following article for more information.