What did Jesus mean by "Before Abraham was, I am"?

⁵¹Verily, verily, I say unto you, If a man keep my saying, he shall never see death. ⁵²Then said the Jews unto him, Now we know that thou hast a devil. Abraham is dead, and the prophets; and thou sayest, If a man keep my saying, he shall never taste of death. ⁵³Art thou greater than our father Abraham, which is dead? and the prophets are dead: whom makest thou thyself? ⁵⁴Jesus answered, If I honour myself, my honour is nothing: it is my Father that honoureth me; of whom ye say, that he is your God: ⁵⁵Yet ye have not known him; but I know him: and if I should say, I know him not, I shall be a liar like unto you: but I know him, and keep his saying. ⁵⁶Your father Abraham rejoiced to see my day: and he saw it, and was glad. ⁵⁷Then said the Jews unto him, Thou art not yet fifty years old, and hast thou seen Abraham? ⁵⁸Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am. ⁵⁹Then took they up stones to cast at him: but Jesus hid himself, and went out of the temple, going through the midst of them, and so passed by.

⁶Even as Abraham believed God, and it was accounted to him for righteousness. ⁷Know ye therefore that they which are of faith, the same are the children of Abraham. ⁸And the scripture, foreseeing that God would justify the heathen through faith, preached before the gospel unto Abraham, saying, In thee shall all nations be blessed. ⁹So then they which be of faith are blessed with faithful Abraham.

¹These words spake Jesus, and lifted up his eyes to heaven, and said, Father, the hour is come; glorify thy Son, that thy Son also may glorify thee: ²As thou hast given him power over all flesh, that he should give eternal life to as many as thou hast given him. ³And this is life eternal, that they might know thee the only true God, and Jesus Christ, whom thou hast sent. ⁴I have glorified thee on the earth: I have finished the work which thou gavest me to do. ⁵And now, O Father, glorify thou me with thine own self with the glory which I had with thee before the world was.