Wifely submission is really just a manifestation of the humility and love that every Christian should have. In the husband, it manifests itself in the instructions to husbands:
"Husbands, love your wives, as Christ loved the church and gave himself up for her, that he might sanctify her, having cleansed her by the washing of water with the word, so that he might present the church to himself in splendor, without spot or wrinkle or any such thing, that she might be holy and without blemish. In the same way husbands should love their wives as their own bodies. He who loves his wife loves himself. For no one ever hated his own flesh, but nourishes and cherishes it, just as Christ does the church, because we are members of his body." - Ephesians 5:25-30
We as Christians are all to be Christlike in love and humility. This is how a husband is to demonstrate this to his wife. In a more general sense, the entire church has these instructions, marriage is no exception to them:
"Do nothing from selfish ambition or conceit, but in humility count others more significant than yourselves. Let each of you look not only to his own interests, but also to the interests of others. Have this mind among yourselves, which is yours in Christ Jesus, who, though he was in the form of God, did not count equality with God a thing to be grasped, but emptied himself, by taking the form of a servant, being born in the likeness of men. And being found in human form, he humbled himself by becoming obedient to the point of death, even death on a cross." - Philippians 2:3-9
A husband's headship and a wife's submission must both stem out of this.
