Who are the souls under the altar in the fifth Seal?
The souls under the altar in the fifth seal are the martyrs, those slain for the word of God and for the testimony they held; they are believers who gave their lives for their faith in Christ.
When the fifth seal is opened, John sees under the altar the souls of them that were slain for the word of God, and for the testimony which they held. These are the martyrs of the faith, those who lost their lives because they held fast to the testimony of Jesus Christ. They cry out with a loud voice asking the Lord how long it will be until He judges and avenges their blood on those who dwell on the earth.
In response, white robes are given to every one of them, and they are told to rest a little while longer, until their fellow servants and brethren, who are also to be killed just as they were, are fulfilled. This shows that more of their brethren on the earth will suffer the same fate before the full number is complete.
The identity of these souls carries great significance. It is the Church, not Israel, that holds the testimony and faith of Jesus Christ, so the fact that these martyrs are crying out for vengeance tells us plainly that the Church is still present on the earth at this point in Revelation. This is why the fifth seal is understood as a foreshadowing of the persecution that will come through the Antichrist, the overthrow of nations, and the desolation of Israel and its Temple, all of which unfold later in the book under the trumpet judgments.
The scriptures
And when he had opened the fifth seal, I saw under the altar the souls of them that were slain for the word of God, and for the testimony which they held: And they cried with a loud voice, saying, How long, O Lord, holy and true, dost thou not judge and avenge our blood on them that dwell on the earth? And white robes were given unto every one of them; and it was said unto them, that they should rest yet for a little season, until their fellowservants also and their brethren, that should be killed as they were, should be fulfilled.
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.