Basically, if you have less then 50 in a stat, then you don't apply for the following.
But once you go over 50 in a trait, you start having the chance to earn a 'paragon' trait. These are extremely powerful traits, that can basically make or break a campaign. But they're still strictly 'local' in effect.
You can also improve the traits, but if you really want to see a major improvement, then you need to get that stat to over 60 and do something extremely important... as well as getting lucky.
If this is done, then you earn a Transcendent Trait. These are basically a Paragon trait taken to the next level. Instead of making or breaking a campaign, you make or break major interstellar empires. You are also now biologically immortal, you can still be killed, but it's much harder, before traits kick in, and even if they do kill you... You are a Transcendent, which means you have a chance to survive none-the-less.
There's a level beyond Transcendent, which is Deity, but that's basically 'Are you the God-Emperor of Mankind? Yes/No? If no, then you'll never reach this. If yes... If you're lucky, but otherwise you'll just stay a Transcendent.
If one of our characters somehow manages to achieve a Deity level trait, then expect it to have been in a massive fight where everyone's attacking us and it's end-game... So much so that the only reason we actually have a chance of winning is because that character reached Deity... and even then, it's probably not a good chance of winning, though at least now we'll probably stale-mate.