One of the verses of scripture I love is in Psalm 2, "he that sitteth in the heavens shall laugh:" Whatever the restless turmoil of man below the view from heaven instantly brings a sense of perspective. The vision of the godly Daniel in Dan 7 really brings that perspective to the vision of the gentile Nebuchadnezzar in Daniel 2. In particular we are introduced to the Son of Man and the Ancient of Days, two figures that we shall see are central to the hope and expectation of every believer in every dispensation. Additionally the promise of an eternal kingdom of God is reiterated in a context that allows us to tie it to some other important scriptural facts.
To pick these verses apart it is best to start with the easiest question, and that is the identity of the Son of Man.
In the Old Testament this title is often used of man in general, especially when the frailty of mankind is being emphasized. The only time it is really used of an individual, and that extensively, is of Ezekiel. Of the 85 references in the New Testament all but four are made by the Lord Himself in the gospels referring to Himself. Some of the more compelling are Mat 24:30 & 26:64 that appear to be references to Dan 7. Of the four others, one is a quote from Ps 8, the other three a reference to the risen Christ.
As Rev 14:14 is a reference to the future and a close quote of Dan 7 it is fairly clear that the Son of Man in Dan 7 is none other than Christ.
The question does remain though, why did the Bible muddy the waters by repeatedly referring to Ezekiel as 'Son of Man'? Of course we don't actually know, but I believe we get a clue if we look at the nature of Ezekiel's ministry. Most of the prophets went around announcing doom upon others and occasionally inflicting punishment themselves. A large part of Ezekiel's ministry was to suffer whilst others watched. He was sent to his own people that would not listen to him. We know that he did not enjoy his work but he did it out of sheer obedience. In a very real sense therefore Ezekiel was a type of the Lord. Obedient to his calling and yet unable to cause heart movement in his own people.
An alternative or possibly complementary explanation is that Ezekiel was granted one of the clearest views of the Lord in the whole of the Old Testament, compared to that vision the inadequacy of mortal man became very noticeable and hence the general name for frail man was applied to a specific individual. The Lord left the glory of heaven and took on mortal flesh and therefore with that same awareness referred to himself as Son of Man.
The far more vexing question then arises; who is the Ancient of Days. If we just had this passage and knowledge of the trinity the answer would appear fairly easy. If the Son is the Son of Man then the Ancient of Days in God the Father. There are a number of reasons for reaching this conclusion: -
Nonetheless there are a few of things that bother me. Firstly we are expressly told that no one has seen God at any time other than through the Son. Secondly the description of the Ancient of Days in Daniel 7 is similar to the description of the Son of Man in Rev 1 and also to the description of 'the likeness of the appearance of a man' in Ezekiel 1. Thirdly the Ancient of Days appears to be judging, we know all judgment has been given to the Son.
The commentators are all agreed that the identification of the Ancient of Days is obvious, however they seem to fall about 50-50 between the Son and the Father! Some of the more eclectic study Bibles will even differ within themselves from page to page.
I think this is one of those instances when we have to accept that we do not understand the nature of the trinity as well as we would like to think. In Isaiah 9:6 one of the titles given to the Son is 'everlasting father'; clearly the Son can sometimes exhibit characteristics that we more naturally associate with the father.
Adam Clarke states that this is the one time in scripture that the father appears in bodily form. I have difficultly overthrowing the words of the Lord that no man had seen the father at any time. Therefore I take it that the Ancient of Days is also a manifestation of the son.
With the players identified we can now turn to the action. A judgment scene is set and the result of that judgment is that an everlasting kingdom, that is inclusive of all nations, tongues and peoples, should be given to the Son of Man.
We are told that this kingdom will never be destroyed, we therefore cannot allow for any attempt to identify it with the 'hearts of all believers everywhere'. Anything dependent upon us is inherently fallible. Daniel would also have understood his own people as partaking of the kingdom promised in v18 so unless this vision was a cruel trick we must assume the kingdom is one in which the Jew has a role. The kingdom here referred to must therefore be the one created through the special action of God after the dispensation of Grace.
We get a clearer picture of how this fits into the overall plan by observing Revelation 5. Here we see a scroll with seven seals, the title deeds to the earth. It is there waiting for one who is worthy, none is found, until finally the Lion of the Tribe of Judah comes forward. This is none other than the Lord as a standing slain lamb. He is then found worthy to take the book and open it because he was slain and because of the multitudes he had redeemed. In other words people whom he has bought with his own blood will populate the kingdom he is given.
Having seen how it fits in, Revelation also provides the when. The opening of the seals happens after the rapture and inaugurates the seven-year tribulation. At the end of the tribulation the son comes to the earth with clouds and wages war with Israel's enemies. The Son of Man wins (of course) and this ushers in the millennial kingdom. Whilst the millennial kingdom ends I judge that the everlasting kingdom starts at the onset of that kingdom. From that point on the Son will be openly acknowledged as such and will rule with a rod of iron.
The question asks for the significance of these actions. In my introduction I suggest that this chapter provides a heavenly view of the age of the gentiles and the everlasting kingdom. The real significance of the vision is simply to show Daniel, and us, that this kingdom is going to happen. God has agreed with himself that his son is going to rule. He has set his king on his holy hill of Zion. Those that attempt to fight this are really imagining a vain thing. 
When Daniel was concerned about the fate of the Jew he was given a vision that God's kingdom would come. When we are concerned about our fate we simply need to remember that God's kingdom will come. Even so, come Lord Jesus. Amen.