Right off the bat, Jesus is making an allusion to Daniel:
I saw in the night visions,
and behold, with the clouds of heaven
there came one like a son of man,
and he came to the Ancient of Days
and was presented before him.
And to him was given dominion
and glory and a kingdom,
that all peoples, nations, and languages
should serve him;
his dominion is an everlasting dominion,
which shall not pass away,
and his kingdom one
that shall not be destroyed.
—Daniel 7:13-14 (ESV)
His favorite self-designation was "Son of Man", which on the surface means that he was human. But by connecting the title with this passage, it also shows that he intended to establish the final kingdom which will outlast all others. The sign was actually a person, "one like a son of man", in Daniel. It seems like the same is true in Matthew:
Then will appear in heaven the sign of the Son of Man,
and then all the tribes of the earth will mourn,
and they will see the Son of Man coming on the clouds of heaven
with power and great glory.
—Matthew 24:30 (ESV)
I reformatted the text to show parallel structure: the Son of Man is the sign. The "tribes of the earth will mourn" because of His "power and great glory". This mourning is also an allusion back to Daniel:
As for me, Daniel, my spirit within me was anxious, and the visions of my head alarmed me.—Daniel 7:15 (ESV)
Here is the end of the matter. As for me, Daniel, my thoughts greatly alarmed me, and my color changed, but I kept the matter in my heart.—Daniel 7:28 (ESV)
The coming kingdom is alarming because it signals the end of existing kingdoms.
Because Jesus warns that these events are eminent ("Truly, I say to you, this generation will not pass away until all these things take place."—Matthew 24:34), one view of the text is that Jesus returned sometime during the first century. This wouldn't be the cross or his resurrection, however, since it seems clear that these events will happen after the events recorded in Matthew. (See also Matthew 16:21-28.) So the most likely guess is the destruction of the Temple in 70 AD.
This interpretation implies that the Roman Empire is the final kingdom, so some preterists conclude that the Parousia is still in the future. Others see the destruction of the Temple in Jerusalem as clearing away the previous system and the establishment of the Church as the final system of reconciliation with God.
Most other interpretations of the passage presume that the Son of Man will appear suddenly and visibly to everyone at once sometime in the future. Two possible parallels would be the star that announced Jesus' birth to the astrologers in Matthew 2 and the angels who announced the birth in Luke 2. But instead of pointing to a human child, the sign would be the coming King Himself: