Your character probably has five core stats, Apocalypse World style. In a normal game, you’ll start with one at +2, one at +1, two at 0, and one at -1. Each stat has associated Basic Moves that you use that stat to roll.
You’ve also got a research log, a journal that reflects what you’ve learned over the course of your journey. It might be a physical diary or notebook that your character keeps, or it might be a numinous thing of memory.
Your log primarily records facts. Facts are specific pieces of information about the world as you’ve experienced it, like “goblins are afraid of fire” or “lavender contains the power of sleep”. Facts are arranged according to topic, a general category of knowledge. “Goblins are afraid of fire” could be a fact about goblins, a fact about fire, or a fact about fear; pick what topic it goes under when you write it in your log. (If you change your mind, you can move facts between topics at end of chapter.)
If a fact in your log is directly relevant to a roll you’re making, that gives you an advantage. For example, knowing that goblins are afraid of fire could give you a advantage when rolling Communication to manipulate some goblins, if you’re using fire and trying to get them to run away.
At end of chapter, write in your log one fact you learned during the chapter, either something you learned about what you encountered or something you learned about yourself.
When you reach three (?) facts on the same topic, you get general knowledge on that topic. This can give you an advantage on a roll when that topic is involved, even if you don’t have a fact that’s directly relevant. If you have both general knowledge and a relevant fact, that gives you two advantages.
When you reach five (?) facts on a topic, you develop a practical application for your knowledge. This gives you a special move related to the topic that lets you do something most people can’t, whether it’s a magical technique, a special physical maneuver, or something else. You can get one move per topic.
The topic of "self" is special. While over the course of your journey you'll learn many things about the world around you and the people, creatures, and spirits that inhabit it, you'll also get new insight into yourself. Learning about yourself gives you a different benefit than the above.
When you have five (?) facts about yourself, you achieve personal improvement. Your greater self-knowledge allows you to improve one of your basic stats by 1. You do this once per five facts about yourself, and you can't improve a stat beyond +3.