After Alexander the Great, Greek became the common language in the occidental world. Even in countries of Semitic culture, most people stoped to speak Hebrew and began to speak greek, at least in intellectual, political and even religious circles. Less privileged people spoke a language derived from the Hebrew: Aramaic. Only educated religious people of Jerusalem would continue to read scriptures in Hebrew. Jews from Egypt had lost the use of Hebrew and, in the first half of the 2d century B.C. produced a (famous) greek translation of scriptures called the Septuagint1 (abbreviated LXX).
During the inter-testamental period2 jewish literature was still produced. Most of it is written in greek and the majority is of the apocalyptic genre. It influenced greatly jewish thinking until the New Testament.
In the LXX, She’ol is translated by hadès (greek: ἁδης), which gave the english "Hades". It is already used by greek philosophy and mythology to talk about the underworld because hadès is the name of the god ruling this place in greek mythology. But the same word does not designate the same thing for pagans than for jews. It is quite important to understand the difference, because the New Testament uses this word and even put it in Jesus’ mouth.
For popular greek thinking, souls are immortal and the underworld is the final destination. People don’t come back from the underworld mainly for two reasons: because they are under custody, and because life for those who are in the good part (the Elysium) is better there than in our world. The place that is assigned to each person depends on the behavior. This can sound culturally familiar to us as later, christianity adopted this view.
In jewish literature like 1Enoch 22; 4Ezra 4,35-36.413; Jubilee 23,304 Hades is divided in two different compartments for the ungodly and the righteous. In 4Ezra 7,36-385 the two compartments in which dead spirits await resurrection and final judgement are named : Gehenna and Paradise. Of course this book is not in the official canon of the Bible, but Paradise and Gehenna are two words used in the New Testament, with the same meaning.
1 Because it was considered to be made by seventy or seventy two jew scholars of the 2d century B.C. who all at the same time produced the same translation of the whole scriptures. The Septuagint is the Bible that first christians used to evangelize the greek world of the first century.
2 This is the time when no official prophecy were written. It is traditionally considered as the last 400 years before Jesus but historically it is the 150 years before Him.
3 35...the souls of the righteous in their tanks have asked, saying: How long do I have to hope for in this way? When shall we reap the fruit of our reward? 36The archangel Hieremiel answered them, "When the number of your fellow men will be complete...
41In Hades, the reservoirs of souls are comparable to the womb. 42For as she who gives birth is anxious to get rid of the strain of childbirth, so these reservoirs are anxious to give back what has been entrusted to them
4 30And the righteous shall see and be thankful and rejoice for ever and ever and see all their judgements and all their curses upon their enemies.
5 36The pit of torment will appear, and opposite it will be the place of rest; the furnace of Gehenna will be shown, and opposite it the paradise of delight. 37Then the Most High will say to the awakened nations, "See and understand him to whom you have said no, or whom you have not served, or whose observances you have despised. 38Look on both sides: here delight and rest, and there fire and torment." Thus will he speak to them on the day of judgement.