The Prayer of Thanksgiving immediately precedes the Words of Institution (or Lord's Prayer, depending on which setting of the Divine Service you are using). This is a prayer that prepares the congregation for the reception of the Lord's Supper. In this prayer, the congregation prays for forgiveness, renewal, and strength.
This prayer is essentially a mealtime prayer on steroids. It's a moment of being gathered together, a moment of recognizing God's mercy and grace, a moment of preparation for the gift we are about to receive.
I imagine the Prayer of Thanksgiving to be like that moment on Christmas Eve or Christmas morning as you sit ready to open the first present. The air is filled with excitement and anticipation. You are more prepared than you ever been to receive this gift in front of you.
Of course the Christmas gifts we receive may be glorious or disappointing. But we are never disappointed by our Lord. His gift of the Lord's Supper always delivers forgiveness, life, salvation, renewal, strength. It is a gift we can always count on and be thankful for.