What did the phrase "son of God" mean to the Jews?
Jesus the Son of God
In the course of 2,000 years of Christian reflection on Jesus, the original Jewish meaning of the title "son of God" has faded and the distinction between "Son of God" and "God" has to all intents and purposes disappeared. In a modern Christian context, "Son of God" is just another way of saying "God". This was not so in the Old Testament and intertestamental Judaism (600BC - 100AD).
Starting at the top of the ladder, the Hebrew bible designates members of the heavenly court as "sons of God" (Job 1:6, 38:7), interpreted as "angels of God" in the Greek translation. A step or two further down comes the historical king of Israel, Solomon, of whom God declares, "I will be his Father and he shall be my son" (2 Sam 7:8-14, The N.T. parallel is John 1:49 "Nathanael answered and saith unto him, Rabbi, thou art the Son of God; thou art the King of Israel."). Next stands every single Jew designated as a "son of God" since the time of the exodus from Egypt, according to the words of the Bible: "Thus says the Lord, Israel is my first-born son" (Exod 4:22). Also, in Luke 3:38, Adam was called "son of God" obviously because he came from God as the creation of God.
In postbiblical times, however, the title "son of God" began to be restricted to pious Jews only. Thus Jesus ben Sira declared in the apocryphal Book of Ecclesiasticus (around 110AD) that only the virtuous and merciful merited this epithet: "Be a father to the fatherless and as a husband to widows, and God shall call you son" (4:10). Moreover, according to the writer of the Book of Jubilee, dating to the middle of the second century B.C. (around 150BC), the Israelites were reckoned "the sons of the living God" provided that their hearts were circumcised and filled with the spirit of holiness (Jub 1:24).
The term "son of God" also became the designation of the awaited royal Messiah. From the 6th century B.C. onward, the descendants of David no longer ruled and the Jews were under Babylonian, Persian, Greek, and Roman dominion. So the earlier promises to the reigning king were reinterpreted as applying to the last "son of David". Thus, for example, "I will be his Father and he shall be my son" (1 Ch 22:10), a divine assurance originally addressed to David's son Solomon, is expounded in a Dead Sea Scroll as referring to the final ruler of Israel. Another Qumran text includes a passage which seems to use the metaphor of God "begetting" the Messiah (1 QS 2:11-12).
So, depending on the context, "Son of God" could point to any Jew, to a pious Jew, to a historical king, or to the future Messiah. When they are considered together, all these designations display one element in common: they are all figures of speech. No biblical or postbiblical Jewish writer ever depicted a human being literally as divine, nor did Jewish religious culture agree to accommodate the Greek notions of special men, born of women but fathered by an Olympian god (thus making them divine). The Greek designations "son of God" and "divine man", common in the terminology of ruler worship in Rome and in the description of extraordinary men in Greek Hellinism, remained taboo to Judaism. These concepts, known from classical mythology but divested of their pagan connotations, may have subconsciously played a part in John's and Paul's formulation of Jesus as God/son-of-God.
In the light of these observations, what does "son of God" signify when applied to Jesus in the gospels? We can be sure it means more than just a pious Jew; it was mostly the equivalent of "Messiah". For example, in Luke 4:41 we find this record; "And devils also came out of many, crying out, and saying, Thou art Christ (Messiah) the Son of God." So now the question exists concerning the definition and boundaries of "messiah".
Messiah (Hebrew; mashiah) means "anointed", specifically with oil, but by extension it meant to be approved and empowered by God for a certain task or position. Thus priests (Ex 28:41 40:15 Nu 3:3), prophets (1Ki 19:16), and kings (1Sa 9:16 16:3 2Sa 12:7) were anointed with oil, and so consecrated to their respective offices. The Greek form "Messias" is only twice used in the New Testament, in John 1:41 ("He first findeth his own brother Simon, and saith unto him, We have found the Messias, which is, being interpreted, the Christ.") and 4:25 ("The woman saith unto him, I know that Messias cometh, which is called Christ: when he is come, he will tell us all things."), and in the Old Testament the word Messiah (R.V., "the anointed one"), as the rendering of the Hebrew, occurs only twice in Daniel 9:25,26 ("And after threescore and two weeks shall Messiah be cut off, but not for himself"). The first great promise in Genesis 3:15 ("And I will put enmity between thee (the serpent) and the woman, and between thy seed (offspring) and her seed; it shall bruise thy head, and thou shalt bruise his heel.") contains in it the germ of all the prophecies recorded in the Old Testament regarding the coming of the Messiah and the great work he was to accomplish on earth (bruising the head of the serpent, the devil).
The following are examples of scripture containing "anointed". The Jews gave these verses a prophetic extension of their meaning beyond what they originally intended. Doing so can be considered a "spiritual interpretation" which can have merit but can also lead to all kinds of excessive recreations of the true intention. So the question is whether the idea of a best and final Messiah to make all wrongs right is a delusion of the Jews or a correct hidden teaching in the scriptures. The gospel writers acclaimed Jesus as the Messiah but the orthodox Jews rejected that idea because Jesus didn't become a worldly ruler that exalted the Jewish nation above all others.
Psalms chapter 2:
In the Old Testament the person anointed with oil was regarded as having been singled out by God as having special powers and functions. As time passed, the term gradually came to refer to a deliverer, himself a descendant of David, who would restore Israel to the golden age she enjoyed under the rule of David. (pg 108+109 of "An Introduction To Christianity" by Alister McGrath)