Edification is the improving of someone's mind or character by teaching them — not stuffing them with facts for a test, but building them up as a person. The word is a noun: the teaching itself, or the good that teaching is meant to do. It is old-fashioned and formal. You are more likely to meet it in a book, a sermon, or a slightly joking remark than to hear a young person say it. Though actually, the Latin underneath is about putting up a building. English kept the 'building' picture and moved it onto the mind. People sometimes use it dryly: 'for your edification' meaning 'so that you know' — not always kindly.