There are really only two theories that I have ever heard. The first is that it comes from Psalms 22. Unfortunatly, I cannot put it on here because it is a long Psalm. Many people think that this Psalm was a foreshadowing of Christ. Even though Christ does not quote the entire thing (as well he couldn’t because he was suffering too much to be able to take the time to quote a lengthy poem), he quoted the important part of it. This Psalm begins with a cry of distress, which is obviously what Christ was in at the moment, but it ends with the knowledge that G-d will triumph in the end. That leads to the second theory that I have heard. Christ was taking all of our sins upon himself. He was suffering the normal physical and psychological pain that would come with being crucified, but he is also suffering a different kind of pain, a spiritual pain that was all too real. Many people think that G-d had to turn his face away from Jesus because of all of the sin that was placed upon Jesus (though Jesus was still perfect because he had never sinned). Basically, it wasn’t necessarily that G-d had abandoned him, but it was that G-d could not “look” at him and had to turn his face away.
Those are the two prominant theories that I have heard. Hope it helps!
That does help! 