@onarum: From what I've gathered second-hand, it's a brewing civil war type thing in one part of the galaxy. I seriously doubt it'd effect anything significantly outside that area; maybe some nearby trade spots.
Nobody really knows how it works, either. There's a big thread on their forums with over 100 people taking part, trying to get the war started, but missions seem to affect reputation / influence randomly and nothing ever seems to happen due to that.
I haven't noticed anything in my corner of Federation space.
That first major event may be a bit different, but from what I've gathered about the influence system, it isn't random. What factors in are the faction itself that is actually asking you to do the job, and what the job entails. For example, I was at an Independent controlled system, whos major influencing faction was a kind of small pirate group (as such slaves, and whatnot, where legal there). However, there is a politcal party there that was still loyal to the Federation, and they had a fetch job up on the board. I took the job and did it, and found that the faction influence had increased by a full percent. Now, that isn't much with just me, but I'm sure if enough people were in that part of space, the system might flip/civil revolt may occur, similar to what we saw in Sol during Gamma.
Also, has anyone gotten guns big enough to take down that capital ship that's going on in the may event?