The word "walked" is a metaphor for the way they lived their lives. To say that they "walked in" their trespasses and sins [verse 1](./01.md) is to say that they often trespassed and sinned. Alternate translation: "because you used to live that way" (See: [[rc://en/ta/man/jit/figs-metaphor]])
The apostles also used "world" to refer to the selfish behaviors and corrupt values of the people living in this world. Alternate translation: "according to the values of people living in the world" or "following the principles of this present world" (See: [[rc://en/ta/man/jit/figs-metonymy]])
"doing what the ruler of the authorities of the air wants them to do." These words expand upon "according to the age of this world." The "ruler of the authorities of the air" is the devil or Satan.