It demonstrates both:
A. The Deity of Christ
B. The Divine Inspiration of the Holy Scriptures
Part A. The Deity of Christ
The Christological significance of the words ‘I AM’ is seen in the Old Testament in Exodus 3:14.
Exodus Three (Septuagint)
11 And Moses said to God, Who am I, that I should go to Pharaoh king of Egypt, and that I should bring out the children of Israel from the land of Egypt? 12 And God spoke to Moses, saying, I will be with thee, and this shall be the sign to thee that I shall send thee forth,-- when thou bringest out My people out of Egypt, then ye shall serve God in this mountain. 13 And Moses said to God, Behold, I shall go forth to the children of Israel, and shall say to them, The God of our fathers has sent me to you; and they will ask me, What is His Name? What shall I say to them? 14 And God spoke to Moses, saying, I - AM - THE - BEING (EGO - EIMI - O - ON); and He said, Thus shall ye say to the children of Israel, THE BEING has sent me to you. 15 And God said again to Moses, Thus shalt thou say to the sons of Israel, The Lord God of our fathers, [The] God of Abraham, and God of Isaac, and God of Jacob, has sent me to you: this is My Name for ever, and My memorial to generations of generations.
Our point of reference is always Greek - the language of the New Testament Scriptures and that of the Church’s Old Testament Scriptures (Septuagint). The words ‘THE BEING’ is to be understood in the context of ‘THE ONE WHO IS’ : Thus I – AM - THE – ONE WHO IS
or I – AM - THE – ONE WHO IS BEING
Exodus 3:14 (Greek) corresponds to Revelation 1:8.
The same four words : EGO EIMI O ON appear in both verses.
εγω ειμι (EGO EIMI) το α και το ω λεγει κυριος ο θεος ο ων (O ON) και ο ην και ο ερχομενος ο παντοκρατωρ. - Apocalypse 1:8.
EGO - EIMI to alpha kai to omega legei kurios o theos O - ON kai o en kai o erchomenos o pantokrator
I - AM The Alpha and The Omega, saith The Lord God, THE – ONE WHO IS, and Which Was, and Which Is To Come, The Almighty. – Apocalypse 1:8
Some particularly interesting instances of ‘I AM’ which are found only in the Gospel of John and exemplify their Theological and Christological significance are as follows:
'Before Abraham was, I AM' – John 8:58
‘Now I tell you before it come, that, when it is come to pass, ye may believe that I AM’. John 13:19
'I said therefore unto you, that ye shall die in your sins: for if ye believe not that I AM, ye shall die in your sins.' John 8:24
'Then said Jesus unto them, When ye have lifted up The Son of man, then shall ye know that I AM ..’ John 8:28
'As soon then as He had said unto them, I AM, they went backward, and fell to the ground.' John 18:6
We may compare these with the following verses which are also unique to John’s corpus where Christ says
I AM :
The Door – John 10:7, John 10:9
The Good Shepherd – John 10:11, John 10:14
The Resurrection, the Life – John 11:25
The Way, The Truth, The Life – John 14:6
The True Vine – John 15:1
The Alpha and Omega, The Beginning and The Ending - Apocalypse 1:8
The First and The Last - Apocalypse 1:17
The Root and The Offspring of David, and The Bright and Morning Star -Apocalypse 22:16
Part B. The Divine Inspiration of The Holy Scriptures
There are exactly 40 times in the Greek New Testament Scriptures where God speaks the words 'EGO EIMI' (I AM).
see http://www.bibleproofs.org/ia.html