Christ (Yeshua) uttered these words while He was hanging on the cross, the last words He spoke before He pronounced "it is finished." What does "Eli! Eli! L'mah sh'vaktani?" mean? The English translation of that phrase is "My God! My God! Why have you deserted me?" So does it mean that God deserted Him in His moments of dire need? Does it mean that He was no longer God? No. No to both of those questions.
Most folks have heard sermons on Christ's death, and most have heard common explanations for this statement. One explanation is that God could no longer look at His Son because He was covered in the sins of the whole world, and God cannot look at sin. Another is that Christ felt so overwhelmed, so alone in that moment, that He cried out in desperation, asking God why He had left Him. Perhaps these are good explanations. Perhaps.
I think that the key to understanding what Yeshua was doing by saying this phrase lies in understanding both the Tanak (Old Testament to most Christians), and the Hebrew mindset and traditions of the time.
Rabbis, even in Yeshua's time, commonly had many pupils or disciples (talmidim in Hebrew) who hung on their teacher's every word. Rabbis called or invited the most promising Torah students to be their talmidim for a Torah cycle (which, in Yeshua's day was approximately three and a half years).
It was common practice for a rabbi teaching his disciples to throw out the first few words of an entire chapter in the Torah that pertains to the lesson at hand. The students would scramble to remember the rest of the scripture, knowing that deeper understanding of the lesson at hand lies within the passage. There was no need for the rabbi to recite the entire chapter, or even to say "look at this book, this chapter." Instead, he'd throw out the first verse. The rabbi knew his students would pick up his meaning, study, and connect it for themselves.
Yeshua from Nazareth was a rabbi. His talmidim called him rabbi. He taught them for a Torah cycle (three and a half years). These men were not just rough, uneducated fishermen (although some of them were fishermen by trade). All men were required to be educated in the Torah, and He called or invited each of them to be his students. And you can be sure that they hung on His every word.
Now picture this: Yeshua is hanging on the cross, nails through His wrists, the weight of His body making his shoulders dislocate. The way His body is hanging, He must push himself up on that nail through His ankles every time He takes a much-needed and labored breath. This is excruciating agony, suffering like most of us have never witnessed. The weight of the world's sins are resting on His shoulders. He's past exhausted, weary unto death from suffering and loss of blood, but His mind is clear and He is going over the prophecies about this moment in eternity. Everything must be complete. Every prophecy concerning His death must be fulfilled correctly. He sees them gambling for His clothes; bystanders are jeering at Him, soldiers mock Him and offer Him vinegar, all unwittingly fulfilling the prophecies about His death with their insults and actions. And our precious Rabbi's mind, the mind of God, reflects on Psalm 22, which begins with "My God, my God, why have you deserted me?" and goes on to prophesy all these things. He pushes Himself up on that nail, takes a breath, and cries out that first line, and the disciples who are within earshot take in a sharp breath. Their minds race over the passage, and the rest of Psalm 22 comes to their remembrance.
How moving it must have been to realize that His last lesson to them was with His very life.