You cannot fully understand the Bible without understanding this word.
The first covenant recorded is between God and every living creature of all flesh that is on the earth (Genesis 9:15). This covenant came after great tragedy and loss in a great flood, but God's covenant was an everlasting agreement not to destroy all flesh by a flood and for the earth to continue having its natural cycles of planting and harvest, hot and cold, and night and day (Genesis 8:22).
This covenant was initiated by God and the conditions for Noah were to restart a new life in faith that God would provide.
In short, a covenant is a permanent (unless broken by one party) commitment between two parties with conditions to believe and act accordingly.
The next covenant was with Abram (Abraham). This covenant came after Abram sacrificed a heifer, a female goat, a ram, a turtledove, and a young pigeon (Genesis 15:9). The covenant gave Abram's offspring a piece of land from the rive of Egypt to the Euphrates river (Genesis 15:18). This covenant was later re-established with his offspring (Isaac, Israel, Moses, and David).
This covenant was also initiated by God and the conditions for Abraham and his descendants were to believe (faith) and walk in the commands of God.
The ultimate covenant in the Bible is the new covenant established by the blood of Jesus (notice that every covenant comes through the shedding of blood). This covenant is between God and everyone who believes and obeys (faith and obedience). As long as a believer continues to trust in God and walk after his ways, they are promised everlasting love and forgiveness in Christ.
With this context, it will be much easier to understand a marriage covenant.
A marriage covenant is also a permanent (unless broken by one party) commitment between two parties with conditions to believe and act accordingly.
The man and woman agree to love, honor, and serve each other until death (when the covenant ends), but both parties must first die to themselves by being crucified with Christ before they can truly honor their covenant (shedding of blood).
What is the process the man and woman go through to make that covenant?
If you are familiar with the Bible, you will notice that it is absent of any dating relationships such as being boyfriend and girlfriend. According to the Bible, you belong to your family or you are one flesh with another party. There is no concept of having a boyfriend/girlfriend (or breaking up).
What is today called premarital counseling is really a modern way of discussing the terms of the covenant and ensuring both parties agree with each other and with God before making their marriage covenant with each other.
This may seem absent of romance, but the Bible does have romance!
The Song of Solomon is filled with romantic language, but all of it is reserved for the bridegroom and his bride. Romance is healthy and important, but only in the context of marriage.
When we have the understanding of covenant, we will never just get a boyfriend and girlfriend for our pleasure. We will discuss the conditions of our commitment and enter into holy matrimony to the glory of God.