[T]here is a sense in which we are always in God's presence, always meeting with him. On various occasions, however, God seems to draw nearer. What the New Testament teaches is that when God's people meet together in the name of Jesus God actually does draw nearer. That is true, whether we feel God's nearness or not. It is his promise, and we should rely on it.
What does "draw near" mean in this context? I have said that it is hard to define, but let me try to clarify the idea somewhat. When God draws near, he has special business with us. As in Isaiah's case [in Isaiah 6], he wants to remind us of his greatness and holiness. He wants us to acknowledge that greatness in our praises. He wants to convict us of sin, and he wants us to confess that sin and receive forgiveness. He wants us to hear his word and obey it. He wants to hear our baptismal and membership vows, and to preside at the discipline of the church. He wants to fellowship with us in the Lord's Supper. He wants to receive our gifts. He wants to acknowledge our unity and love for one another as his body. For such purposes, God draws near. And from such fellowship with God in the name of Christ, we arise, empowered by his Spirit, to do his bidding.
-- John M. Frame, Worship in Spirit and Truth, p. 34