What is the great multitude that comes out of great tribulation?
The great multitude that comes out of great tribulation is the Church, the redeemed people of God from every nation who stand before the throne in white robes, having washed those robes in the blood of the Lamb.
Revelation 7:9-14 describes a great multitude, so vast that no man could number it, gathered from every nation, tribe, people, and tongue. They stand before the throne and before the Lamb, clothed in white robes and holding palms, crying out, "Salvation to our God which sitteth upon the throne, and unto the Lamb." When one of the elders asks who they are and where they came from, John is told plainly, "These are they which came out of great tribulation, and have washed their robes, and made them white in the blood of the Lamb."
This multitude is identified as the Church. It is the Church that is in Heaven, having come out of great tribulation, and this is described as the word of truth that the Body of Christ must either accept or continue to reject. Their robes are washed and made white specifically in the blood of the Lamb, showing that their standing before God rests entirely on Christ's sacrifice.
Because they have come through great tribulation, they are given a special place of rest and service. Revelation 7:15-17 shows that they are before the throne of God, serving Him day and night in His temple, and that God Himself dwells among them. They shall hunger no more, neither thirst any more, neither shall the sun light on them nor any heat, for the Lamb shall feed them and lead them to living fountains of waters, and God shall wipe away all tears from their eyes.
This great multitude in white robes is distinct from the 144,000 who are sealed from the twelve tribes of Israel at the same point in the timeline, following the sixth seal. While the 144,000 are Jewish men who are sealed and raptured, the great multitude represents the Church, redeemed from among all nations, rejoicing before the throne after having endured and come out of the great tribulation.
The scriptures
After this I beheld, and, lo, a great multitude, which no man could number, of all nations, and kindreds, and people, and tongues, stood before the throne, and before the Lamb, clothed with white robes, and palms in their hands; And cried with a loud voice, saying, Salvation to our God which sitteth upon the throne, and unto the Lamb. And all the angels stood round about the throne, and about the elders and the four beasts, and fell before the throne on their faces, and worshipped God, Saying, Amen: Blessing, and glory, and wisdom, and thanksgiving, and honour, and power, and might, be unto our God for ever and ever. Amen. And one of the elders answered, saying unto me, What are these which are arrayed in white robes? and whence came they? And I said unto him, Sir, thou knowest. And he said to me, These are they which came out of great tribulation, and have washed their robes, and made them white in the blood of the Lamb. Therefore are they before the throne of God, and serve him day and night in his temple: and he that sitteth on the throne shall dwell among them. They shall hunger no more, neither thirst any more; neither shall the sun light on them, nor any heat. For the Lamb which is in the midst of the throne shall feed them, and shall lead them unto living fountains of waters: and God shall wipe away all tears from their eyes.
And I beheld when he had opened the sixth seal, and, lo, there was a great earthquake; and the sun became black as sackcloth of hair, and the moon became as blood; And the stars of heaven fell unto the earth, even as a fig tree casteth her untimely figs, when she is shaken of a mighty wind. And the heaven departed as a scroll when it is rolled together; and every mountain and island were moved out of their places. And the kings of the earth, and the great men, and the rich men, and the chief captains, and the mighty men, and every bondman, and every free man, hid themselves in the dens and in the rocks of the mountains; And said to the mountains and rocks, Fall on us, and hide us from the face of him that sitteth on the throne, and from the wrath of the Lamb: For the great day of his wrath is come; and who shall be able to stand?
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.