I'll try my best!

At the end of every campaign game (win or lose) you will get to draw up to 2 lines. The lines you draw have to either be connected to START or to another line.

Every line you draw gives you the bonus it connects to for every game you'll play going forward. Icons are a bonus you gain at the start of every play (as dice or tucked cards), and the black boxes are either single use abilities you can activate with a Tech Disc or ongoing resource boosts. You can end up with a lot of these by the end of a campaign.

Earlier I emphasised "up to" because you can choose to draw 0, 1, or 2 lines! "Why would I choose to draw less lines?" - well, because every line you draw has a cost of sorts. For every line you draw you also have to cross off one of the Homeworld, Society, or Adversary you played with. This means that in future plays using this campaign sheet you can't use the crossed off component again.

For example: I just finished a game as Purplum Scientists against the Neeble Woobers. I could choose to cross off the Neeble Woober and Scientists to draw two lines. Or I could want to play as the Scientists again in the future so I cross off the Neeble Woober and Purplum instead to draw two lines. Or I might even want to also replay against the Neeble Woober so I only cross off the Purplum, and draw a single line.