Scripture does not give us a great deal of information regarding a temporary place of the dead. We actually learn the most from Luke 16:19 and following, so a careful study of that passage would be most helpful.
Let me stress that Scripture says nothing about a place called purgatory. That is a Catholic doctrine, but one that is not supported by the Bible. The Bible teaches that at death unbelievers go to a place of torments called Hades or Sheol in the Old Testament. It is a temporary place of torment where unbelievers remain until they are resurrected to face the Great White Throne Judgment of Revelation 20. From there they will be cast permanently into the eternal lake of fire.
On the other hand, the Bible teaches that believers go immediately to heaven. Before Christ’s death on the cross for our sin, it was called Abraham’s Bosom. Today, the New Testament declares that believers go directly into the presence of the Lord (cf. Phil. 1:21-24 with 2 Cor. 5:1f). Believers will be resurrected to face the Bema or Judgment Seat where they will be held accountable for this life. At that point their works will be evaluated and, based on the nature of those works, they will either receive rewards or lose rewards.
We have a couple of studies on our site called, The Judgments (Past, Present & Future), and The Doctrine of Rewards, located in the “Eschatology” topic section that you might want to check out for more detail.
Below is a short explanation of Luke 16 from The Bible Knowledge Commentary which I hope will help.
16:19-21. Jesus then told the Parable of the Rich Man and Lazarus to show that being rich should not be equated with being righteous. The rich man had everything he wanted. Purple referred to clothes dyed that color, and fine linen was worn for underclothes; both were expensive.
A poor man, a crippled beggar named Lazarus, had nothing. One lived in luxury for himself, the other in abject poverty with hunger and poor health (sores). Perhaps Jesus picked the name Lazarus because it is the Greek form of the Hebrew name which means “God, the Helper.” Lazarus was righteous not because he was poor but because he depended on God.
16:22-23. In the course of time both men died. Lazarus went to Abraham’s side while the rich man . . . was buried and was in hell, a place of conscious torment (vv. 24, 28). Hade„s, the Greek word often translated “hell,” is used 11 times in the New Testament. The Septuagint used hade„s to translate the Hebrew (the place of the dead) on 61 occasions. Here hade„s refers to the abode of the unsaved dead prior to the great white throne judgment (Rev. 20:11-15). “Abraham’s side” apparently refers to a place of paradise for Old Testament believers at the time of death (cf. Luke 23:43; 2 Cor. 12:4).
Definitions of ‘hell’ and related words might help as well:
HELL In common usage, this term refers to the place of future punishment for the wicked. The word properly translated “hell” in the New Testament is the Greek Geenna or Gehenna, a place in the valley of hinnom where human sacrifices had been offered and where continuous burning of rubbish made it an apt illustration of the eternal lake of fire (cf. Matt. 5:22). Other words like sheol or hades are improperly translated by this term.
SHEOL The general idea of this word is “the place of the dead” including the grave (cf. Num. 16:30,33; Ps. 16:10), and the unseen place of those who have departed from this life, the place of departed spirits or both the righteous (Gen. 37:35) and the wicked (Prov. 9:18).
HADES This word is basically the New Testament counterpart of the Sheol. It refers to the unseen world in general, but specifically to the abode of the unsaved dead between death and the final judgment at the great white throne (cf. Luke 16:23 and Rev. 20:11-15). It differs from hell or Gehenna in that it is temporary while hell is permanent.
LAKE OF FIRE Refers to the eternal state of the wicked who are forever separated from God and consigned to a special abode of suffering because of their rejection of Christ or their lack of the righteousness of Christ. It is equivalent to and identified with the second death in Revelation 20:14.