Why are the 144,000 sealed?
The 144,000 are sealed as servants of God so that they are marked and protected before God's wrath is poured out on the earth, and so the harm coming through the trumpet judgments will pass over them.
Scripture shows that before the wrath of God can be poured out on the earth, certain things must happen first. The Church must still be present, since it is not appointed to God's wrath, and the 144,000 must be sealed. Revelation 7 tells us that an angel ascending from the east cries out to the four angels who have power to hurt the earth and the sea, saying, "Hurt not the earth, neither the sea, nor the trees, till we have sealed the servants of our God in their foreheads." This shows that the sealing is tied directly to holding back harm from the earth. The angels are not permitted to bring destruction until this sealing is complete, which means the seal marks out these 144,000 as belonging to God and as those who must be preserved before judgment can proceed.
The purpose of the seal becomes even clearer later in the judgments. When the locusts are released from the bottomless pit, they are commanded not to hurt the grass, any green thing, or any tree, but only those who do not have the seal of God in their foreheads. Since the 144,000 were sealed by the Angel of the Lord, the locusts pass over them because of that seal. So the seal is what identifies them as belonging to God and shields them from that specific torment that comes upon the rest of the earth.
In this way, the sealing of the 144,000 serves two purposes together: it marks them out as the Lord's own, and it sets a boundary of protection so that the destructive forces released afterward, such as the locusts, cannot touch them because they carry the mark of God rather than being without it.
The scriptures
And I saw another angel ascending from the east, having the seal of the living God: and he cried with a loud voice to the four angels, to whom it was given to hurt the earth and the sea, Saying, Hurt not the earth, neither the sea, nor the trees, till we have sealed the servants of our God in their foreheads. And I heard the number of them which were sealed: and there were sealed an hundred and forty and four thousand of all the tribes of the children of Israel.
And it was commanded them that they should not hurt the grass of the earth, neither any green thing, neither any tree; but only those men which have not the seal of God in their foreheads.
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.