Pope Gregory I is significant in a number of ways.
First, he is significant for having increased the secular power of the papacy. Gregory took temporal power over an area that came to be known as the Papal States. He did this as a way to help keep Rome safe from invasions of the time, but it ended up establishing the Church as a temporal power.
Second, Gregory did a great deal to spread the faith. He is responsible for sending missionaries to Britain, for example, to convert the people of that Island.
Finally, Gregory worked to create a unified Church with a unified belief system and liturgy. He was energetic in trying to reduce the amount of heresy in the Church. He made changes to the liturgy and encouraged their use across Europe.
In these ways, Gregory I was important for having increased the power and the unity of the Church.