Chapter six began already back in chapter five, which called Christians to demonstrate our reverence for Christ by living in submission to one another (v21). The chapter went on to describe the submission married couples live in (wives to their husbands, and husbands to Christ). Chapter six continues this call for submission.
v1-9 - Christian submission extends to all aspects of life:
Children must continue to demonstrate the submission modeled in the fifth commandment to honor your father & mother (v2).
Fathers hear an echo of Proverbs 22:6 to bring their children up to fear the Lord.
So far the call for submission has been limited to family relationships, but starting in v5, Paul busts the door open in a big way: your Christian life of submission is not just limited to what happens under your own roof, but extends to all of life's activities. (Paul addresses slaves and masters, but the slavery of Roman society was very similar to the employee-employer relationships we have today, so this very much applies to your work setting as well).
Employees: work as if you were working for Christ Himself, because of the tremendous promise that's made to you here. You've got much more than just a paycheck coming your way:
The Lord will reward each one for whatever good they do (v8)
Employers: realize that you are just as much in submission to the Lord as your employees are, so do your work well, and treat your employees accordingly.
v10-20 - This is the famous passage regarding the Armor of God. The overarching command here comes in the opening line:
be strong in the Lord and mighty in His power (v10)
Before telling you how to do this, Paul tells you why you need to do this.
The devil is scheming against you, and you need to stand against them.
Whether you realize it or not, you're in the midst of a tremendous struggle.
This struggle is much more than the day to day problems that we all face.