Paul takes his readers from their living a wholesome life before the Lord to their personal relationships with one another. He brings up the word "submission." Believers are to live submissive lives to one another.
Ever since Christ taught His disciples about how to be "great" in His kingdom He has always focused on their humility to each other and their obligation to serve one another. He used Himself as the Prime Example in Matthew 20:28, "I came not to be served, but to serve and to give My life a ransom for many." He was the Lord of all, but He chose to live His life amongst man as a servant to all! And we should do no less.
Now note this, the effects of being filled with the Spirit are seen as singing praise to God and being thankful for all things. But this verse is also part of the effect of the Spirit's filling. The believer will find the Spirit leads them to be submissive to one another, placing others as better than themselves, Philippians 2:3. Believers are expected to be humble and reverent to their Savior, but that also means they will be humble and respectful to their brothers and sisters in Christ.
Submissiveness is not being a "doormat to be stepped on" and put down, but to be a stepping stone to allow someone else to be lifted up! When you submit to Christ you're not just expecting that you will be obedient to Him. You're really seeking to honor Him in all you do that He will get the praise! When we submit to one another we are seeking to lift each other up in "honor, preferring one another," Romans 12:10 KJV. Nothing wrong with that.