Main Plot Events are events that are very important to the world of 75-SOL. While they are not mandatory to participate in, it is very recommended.
Finished Plot Events can have several kind of effects such as an expansion of the world map(new places to visit), new Shops/new shop items as well as whole new kinds of species. Aside from that, you can gain gold as bonus reward for your character(Heroes get twice the amount of gold due to their job!!) and sometimes, your character can also develop his skills by participating.