One of the verses that Jesus spoke in Aramaic instead of Greek.  For more on the topic of Jesus speaking Greek, please refer to this article.

Many people reading this verse today think that means that Jesus felt alienated from his Father at the time of his death. The Jews of his era, would have recognized it for what it really is, the first line of Psalm 22, which makes several specific statements prophetic of the Annointed's death, including his garments being divided by lots. Because this line is a quote, we have four sources for this verse, the Hebrew Psalm, the Greek Psalm, and the Greek NT both here and in Mark. If you read the Psalm (an English translation here), you can see why he was quoting it: it was a description of his death. 

In other words, Jesus is reminding those around in and who would read his words, that the suffering he was going through was foretold and, as he said many times, required to fulfill the prophecies. 

These two observations lead to an important third: the close correspondence between Jesus's quotes of scripture and the Greek Septuagint is not an artifact of translators using the Septuagint to guide translation. In this case, the Greek of the Septuagint is very different than the Greek of Matthew, even though there are only a few words involved. This demonstrates how unlikely it is that Jesus's other, much longer quotes of the scriptures could be nearly word-for-word identical to the Septuagint if it was not the form that Jesus was actually quoting.

The Greek word translated as "God" means "God" and "deity." It is not introduced with an article, which would makes it "the Divine." Jesus usually used it uses this word for God with the article before it, perhaps to indicate the one God as opposed to the pagan gods. In this case, the Greek here is more literally "God of mine, God of mine," but the Greek of the Septuagint is different, ὁ θεὸς ὁ θεός μου, or "The Divine, the Divine of mine." Again, this is the way Jesus's statements in Greek about God are normally recorded, as opposed to this translation by Matthew from the Aramaic. In the original Hebrew of Psalm 22, there is neither "the" nor "my." The text is the simple "El," which means "God" or "Might one."

Jesus, however, seems to have blended the Hebrew and Greek versions in his Aramaic. Note the Aramaic in the first part of this verse. Here, the word for God is "Eloi," which is the Aramaic word for God, "El" followed by the suffix "oi" which indicates "my." So, in speaking Aramaic, Christ was closer to the Greek translation, which added poetic niceties to the bare bones Hebrew. However the Septuagint of Psalm22, two Greek words appear before the Greek translated as "why" that are not in Jesus's Aramaic. These words are a verbal command meaning "hold before me" or "surpass me" are ignored by Jesus and do not appear in this place in the Hebrew.