Here, Peter is describing the duties of husbands and wives to each other, but begins with the wife. The apostle is talking about the wife's submission to her husband in the home.
In the past, whenever I heard the word "submission" in the Bible, in regards to women submitting to their husbands, it would immediately provoke a slew of emotions in me because I viewed the word to be just as the dictionary states it - "the action or fact of accepting or yielding to a superior force or to the will or authority of another person" and my feministic nature kicked in. I was not going to submit to my husband or any other person who wanted me to yield to them, especially if I didn't agree. And yet, I had professed my life to GOD and was willing to put him first in my life by following him and essentially submitting to his will, but beyond that, NO WAY!
Peter is not asking women to be submissive to their husbands as a way to make men superior to women, but instead, suggests that if a woman adopted a different religion back in the day when this was not common (such as following Jesus), they needed instructions on how to bring their husbands to Jesus. Peter encouraged women to not use their outward beauty with fancy hair braids, gold jewelry and fine clothes to win over their husbands, but instead, to use the beauty of their inner self and "the unfading beauty of a gentle and quiet spirit, which is of great worth in God's sight". Peter was calling women to live such good lives with their husbands, that they may be won over by the wife's actions and showing the life of GOD in them, this was a way to introduce unbelieving husbands to the life and work of Jesus.
God's plan is one where he wants each of us to forsake our own desires and live for Christ, not ourselves. So in this Chapter, and in God's order, Christ is the head of the husband, and the husband is the head of the wife. The wife then submits to her husband who is called to lead and serve his wife while he simultaneously submits to Christ
Being submissive which includes being humble, deferential, cooperative, loyal and respectful is a characteristic of Christ like living. As believers, the life of God in us, is about cooperating, taking on responsibility and carrying burdens for each other, even if others we are surrounded by don't yet believe. We submit, in order that the life of GOD might be seen in us and that those who see that life, might glorify GOD on the day he visits us.