From John 10:7, this article shows that when Jesus said, "I am the door of the sheep," he was pointing to himself as the means to receiving eternal life, the source of knowledge of God, and the fount of spiritual nourishment.
When Jesus Christ stood and said "I am," he was pointing to his deity. From John 6:35 this article shows that when Jesus said "I am the bread of life," he was pointing to himself as fundamental to life, as the fulfiller of life, and as the formula to life.
This paper considers the significance of Yahweh revealing himself as "I am" in Exodus 3:13-14. Jesus' use of a similar expression to refer to himself a number of times is read in the light of Exodus 3.