From: Vermont, USA
Let's take a look at Rek Ixito, the Leader of our new Zenox Technocracy. You'll note that he is ruling from our Capitol. That's where you want to keep your Leader if you want him/her/it to be effective. Leaders have effects that influence your entire faction, every planet, base, construction project, etc. so they are very important in that respect. In some cases (for example, dictatorship or hive mind factions) you may have the same leader for a long period of time. In other cases (for example democracies or republics) your leader may chance on a regular basis as the result of elections. Characters can also be lost due to more violent events (for example, a new despot deposes the old despot, or the Dhayut turn your capitol planet into a radioactive wasteland), accidents or eventual retirement.
Each character has some skill areas. In this case, Rek Ixito increases our Colony Happiness by 8% and our Tourism Income by 17%. He seems to be a generally benevolent sort of leader. Next to each of these skills is a progress bar, that measures progress towards the next advancement in that skill. You can increase skills through experience in areas related to those skills. You can also acquire new skills the same way.
You may also note that Rek has a "trait", in this case he is Famous. Your characters may start with one or more traits and may acquire more based on their experiences. In this case, Famous increases Colony Happiness and Tourism Income, so it meshes well with Rek Ixito's existing skills. There is a tool tip not visible in this screenshot that explains how much each trait contributes to the listed skill levels.
Let's take a look at the other character that we started with in this test game, Randul Shokia, a Scientist.