With the Shofar, we are accomplishing many things. Let us focus on one aspect.
Renewal of the Mochin (spiritual abundance that is the food and sustenance of the spiritual world). with the Shofar, we have the strength to renew the Mochin. This new Mochin is sweetening all of the Mochin that were previously within the spiritual worlds.
We have the opportunity to elevate all the spirituality that is within us getting to a level of something new that we never had before and then bring it all back to its place within the spiritual worlds. This is accomplished with the shofar.
In other words, we have the opportunity on Rosh Hashanah to receive new levels of spirituality that we never experienced before. You have this power the whole 2 days of Rosh Hashana, but specifically during the prayers and the shofar you have an even stronger power to bring yourself higher.
Remember its not only another day of long prayer, it is the prayer that you are praying for the whole year.