The festivals of God reveal His plan for the salvation of mankind in a step-by-step manner. Once you understand them, you can explain God's plan from beginning to end.
Briefly, the meanings of the biblical festivals are as follows:
Passover reminds us of the sacrifice of Jesus Christ to pay the penalty for our sins.
The Days of Unleavened Bread point us to the need to seek God's help to live a sinless life based on the Ten Commandments and the other laws of God.
Pentecost reminds us of the pouring out of God's Holy Spirit upon His people and the founding of the Church. It reminds us that this is not the only day of salvation. It is the time of evaluative judgment of those God is calling at this time.
The Feast of Trumpets reminds us of the coming of Jesus Christ at the sounding of the seventh trumpet, and the resurrection of those who have responded to God.
The Day of Atonement pictures the binding of Satan. Besides showing Satan's responsibility in instigating sin, it reminds us of Christ's sacrifice for all mankind, which makes it possible for man to be reconciled to (or made "at-one" with) God.
The Feast of Tabernacles represents the 1,000-year reign of Jesus Christ on the earth.
The Last Great Day represents the second resurrection when all those who never had the opportunity to understand God's way of life will be given that opportunity.
The explanation above does not include scriptural references, so the details are missing. To better understand the festivals of God, we recommend you read God's Holy Day Plan: The Promise of Hope for All Mankind.