Let's start off with the base stats (Strength, Endurance, etc). 1 represents an average human. A strength of 2 would mean that the person is twice as strong as an average human, 3 would mean 3 times... and so on.
Now we get onto the skills (Martial, Diplomacy, etc). The more stars MC has in a skill, the higher the level of that skill. Duelling skill compares MC's fighting ability to the rest of the world. Martial represents a person's ability to lead in battle, Diplomacy represents the person's ability to negotiate deals, Stewardship represents the person's ability to store and produce money, Intrigue represents the person's ability to create plots and find out secrets (scheming and manipulation too) and finally, Learning is a measure of a person's knowledge.
Traits are well... traits. They affect base stats, an example would be the trait genius. Genius adds +2 to intelligence.
Level-ups happen when MC does something noteworthy (such as defeating the Usurper). Every level gives a +0.1 to the skill that the level-up was mainly based on. For example, looting tons of ships would either give martial or charisma (or in some cases both).
Well... that's pretty much it, I can't think of anything else to write here.