There is an epic war between the Sith (Sith Empire) and Jedi (Galactic Republic). The timeline has revealed that the Sith took Coruscant rather dramatically and forced the Galactic Republic to sign a treaty. The treaty isn't really working though and there are battles taking place in the outer rim. The Jedi have relocated to Tython (where the force was first discovered) and rebuilt a temple. The Threat of Peace comic showed that following the treaty things were pretty tense, and that both sides were itching to battle.
Based on what I've gleaned from the releases in classes, planets, timeline entries, etc., the character you play will fill the "hero" role on either side you align with, with the option of making decisions that will alter your future as a dark-sider or light-sider. The battles you go through will influence the war.
As for PvP, we haven't heard anything on that front yet.