The engagement period is the time from the initial commitment of the couple to each other until the wedding day. One scriptural example is the story of Joseph and Mary. In the Jewish tradition, engagement or "betrothal" was a one-year period. The commitment was binding, and the only thing that could break it was unfaithfulness. Thus, when Mary was found to be with child, Joseph intended to break the betrothal until God supernaturally revealed the truth to him.
During the engagement period, the couple has time to prepare for marriage. In additional to physical preparations such as a home of their own, they must make adjustments in their thinking as they consider their future life together. Up to that point they have only had to think of themselves. They did not even know if they were going to get married, and may have never considered some things. There are big adjustments on both sides, which take time. God has allowed time for these to take place. If both husband and wife allow God to prepare them, the beginning of their life together will be a wonderful experience.
God is working this same thing in the church. Our initial commitment to God is the beginning of our engagement to Him. I believe this is what Paul refers to in Ephesians: "In Him you also trusted, after you heard the word of truth, the gospel of your salvation; in whom also, having believed, you were sealed with the Holy Spirit of promise, who is the guarantee of our inheritance until the redemption of the purchased possession, to the praise of His glory." (Ephesians 1:13-14)
The marriage supper of the Lamb has not yet taken place. This is the time of preparation. Our faithfulness to Christ is being proven. The Holy Spirit has been given as a guarantee or "down payment" of our inheritance. God is serious about His commitment, and He has given of Himself to show that He is serious. He is preparing His bride for Himself that "He might present her to Himself a glorious church, not having spot or wrinkle or any such thing, but that she should be holy and without blemish." Our marriage to Christ has not yet been consummated. At the marriage supper of the Lamb, the matter will be settled for all eternity.
Can we allow this to speak to us and make us more serious about the time we live in? So many take this relationship with Christ very lightly. We play with unfaithfulness, thinking it will not matter. Jesus said that he who is a friend of this world is an enemy of God. What if a bride flirts with other men during the engagement period? What if her future husband keeps looking at other women to see if there might be somebody better? What will happen after marriage? Will this change? That is the reason for the engagement period: to allow the initial commitment to affect every area of life and be proven, so that on the wedding day when the marriage is consummated there is purity in the relationship.
I believe if a couple will take Christ and the church as their example during engagement, it will provide light to walk in to make this time very meaningful. While there are certainly some practical matters to be attended to, the primary preparation is in their relationship with God. If both diligently strengthen their relationship with God during this time, it will form the solid foundation that is needed on the marriage day and for the rest of their life together.