Marriage itself is a special God-approved agreement or covenant between one man and one woman, as in the case of Adam and Eve (Genesis 2:18, 21 - 24). The Eternal made possible this special relationship after creating Eve especially for Adam. Although a number of Old Testament individuals had more than one wife, the New Testament reaffirms God's original intent.
The marriage covenant is a commitment to live together to maintain a home, to share sexual intimacy, and (many times) to produce children and raise a family. This union is intended to be permanent and should not cease, ideally, until death.
The Bible NEVER says anything specifically about being joined in matrimony "in the heart." If this means emotional affection is required, this often came after the ceremony, not before (cf. Genesis 24:67). Consensual agreement must be involved before a marriage occurs.
In order to be wed in God's eyes, some kind of verifiable contract or license needs to be signed before witnesses. The couple's present feelings of wanting to be together forever are not enough by themselves. Matrimony is not only an individual contract that concerns the couple in question, which is often a popular notion in individualistic Western countries like America, it also impacts society in general. A man and woman who lives together and has sex, without the benefit of making their vows of love 'official,' is living in sin (called 'fornication' in the King James Translation).
Important scriptures related to marriage include Genesis 2:18, 21 - 24, Malachi 2:14 - 15, 1Corinthians 7:1 - 17, Ephesians 5:22 - 33, Colossians 3:18 - 19, Hebrews 13:4, and 1Peter 3:1 - 7 among many others.
Once a woman has forgiven a man,
she must not reheat his sins for breakfast.
(Marlene Dietrich, 1901 - 1992)
Keep your eyes wide open
before marriage, half shut afterwards.
(Benjamin Franklin, 1706 - 1790)