What I Learned
The husband is the "Head of Household" (which some feel is like, say, the President of the United States and others believe should be a dictatorship).
The husband is the "main bread winner" and is responsible for providing for and protecting the family.
The wife is the "weaker vessel" and accountable for training up the children, cleaning up after her husband (and serving him in other ways i.e. making and bringing him his dinner, ironing his clothes, etc.) and overall maintaining and condition of the household.
The wife "submits" to her husband and sacrifices her own wants and ways of doing things for those of her husband. Few say if a marriage resembles more of a "master/slave" relationship the wife is still required to "submit" to her husband though others disagree with this assessment.
A wife is called to be submissive yet wise. If her husband asks her to sin, she is to respectfully decline.
A husband answers for his family before God. Though various jobs are delegated to members of the family, it is the "man of the house" who has to supervise and make sure all for whom he is responsible live up right, according to the Word of God, in a manner that is pleasing to Him.
What the Bible States
(Warning: This could very well end up being a multi part post.)
22 Wives, submit to your own husbands, as to the Lord. 23 For the husband is the head of the wife even as Christ is the head of the church, his body, and is himself its Savior. 24 Now as the church submits to Christ, so also wives should submit in everything to their husbands.
25 Husbands, love your wives, as Christ loved the church and gave himself up for her, 26 that he might sanctify her, having cleansed her by the washing of water with the word, 27 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. 28 In the same way husbands should love their wives as their own bodies. He who loves his wife loves himself. (Ephesians 5:22-28. ESV.)
2 But because of the temptation to sexual immorality, each man should have his own wife and each woman her own husband. 3 The husband should give to his wife her conjugal rights, and likewise the wife to her husband. 4 For the wife does not have authority over her own body, but the husband does. Likewise the husband does not have authority over his own body, but the wife does. 5 Do not deprive one another, except perhaps by agreement for a limited time, that you may devote yourselves to prayer; but then come together again, so that Satan may not tempt you because of your lack of self-control. (1 Corinthians 7:2-5. ESV.)
3 But I want you to understand that the head of every man is Christ, the head of a wife is her husband, and the head of Christ is God....8 For man was not made from woman, but woman from man. 9 Neither was man created for woman, but woman for man. 10 That is why a wife ought to have a symbol of authority on her head, because of the angels. 11 Nevertheless, in the Lord woman is not independent of man nor man of woman; 12 for as woman was made from man, so man is now born of woman. And all things are from God. (1 Corinthians 11:3 & 8-12. ESV.)
10 An excellent wife who can find?
She is far more precious than jewels.
11 The heart of her husband trusts in her,
and he will have no lack of gain.
12 She does him good, and not harm,
all the days of her life.
13 She seeks wool and flax,
and works with willing hands.
14 She is like the ships of the merchant;
she brings her food from afar.
15 She rises while it is yet night
and provides food for her household
and portions for her maidens.
16 She considers a field and buys it;
with the fruit of her hands she plants a vineyard.
17 She dresses herself with strength
and makes her arms strong.
18 She perceives that her merchandise is profitable.
Her lamp does not go out at night.
19 She puts her hands to the distaff,
and her hands hold the spindle.
20 She opens her hand to the poor
and reaches out her hands to the needy.
21 She is not afraid of snow for her household,
for all her household are clothed in scarlet.
22 She makes bed coverings for herself;
her clothing is fine linen and purple.
23 Her husband is known in the gates
when he sits among the elders of the land.
24 She makes linen garments and sells them;
she delivers sashes to the merchant.
25 Strength and dignity are her clothing,
and she laughs at the time to come.
26 She opens her mouth with wisdom,
and the teaching of kindness is on her tongue.
27 She looks well to the ways of her household
and does not eat the bread of idleness.
28 Her children rise up and call her blessed;
her husband also, and he praises her:
29 “Many women have done excellently,
but you surpass them all.”
30 Charm is deceitful, and beauty is vain,
but a woman who fears the LORD is to be praised.
31 Give her of the fruit of her hands,
and let her works praise her in the gates. (Proverbs 31:10-31. ESV.)