Each empire, that comes, appears out of nowhere, or because you went to sandbox mode, is perfectly normal, but when you look at the top right corner you see a colored box near an empire's name. This box is an empire's special trait. These traits give empires certain advantages and disadvantages.
Sometimes, empires are born with multiple traits. All traits affect the empire and quite often these empires beat other empires that don't have any traits.
Science/Sci(Dark Blue) Edit
Gains research bonus.
Build Science ships.
More likely to make peace, and other relations bonuses.
Gains defense bonus, and more likely to make peace.
Build Gun boats.
Gains combat bonus, but receives research penalty.
Builds more (and bigger) ships, develops faster.
Unlikely to change political state.
Unstable/Uns(Light Gray) Edit
More likely to change political state.
Combat bonuses early, but grows weaker as it ages.
Fanatic/Fan(Light Pink) Edit
No research, but military bonus, and automatically transcends after some time.
Aggressive/Agg(Dark Red) Edit
Gains attack bonus, but receives a research penalty.
Reclusive/Rec(Dark Gray) Edit
Prefers to stay out of the limelight, but good at defense and research.
Slow Starter/Slo(Light Brown) Edit
Combat penalties early, but gradually becomes normal.
Great at managing and wealth.
Really aggressively expansive but will not develop their stars.
Don't build ships.