The life of the Holy Spirit is a life in which a Christian can experience the Holy Spirit living in him and working throught him.
Most Christians today are not living the life of the Spirit. They live their Christian lives on the basis of doctrine. They were taught about Christ and about how to live trying to pattern their lives according to Christ's teaching. They believe that Christ is real and that he hears them and helps them. BUT they do not feel that they are in much contact with Him. They do not experience Christ's presence nor do they see things happen which they can tell are His workings.
The life of the Holy Spirit changes that.
When a person is living the life of the Spirit, he knows by experience that the Holy Spirit is in him.
When a person is living the life of the Spirit, he begins to experience the Holy Spirit making it possible for him to praise God and worship God with a new freedom.
He experiences the Holy Spirit making the scriptures come to life and catholic doctrines make sense. Amazingly, he experiences a new ability to talk to people about Jesus Christ with a deeper peace and joy.