The Rabbinic interpretation is:
- "Ancient of Days" is a name of God
- "son of man" is a mistranslation
The Biblical Hebrew term "ben adam" or its Aramaic equivalent "bar enosh" is used for a mortal, fallible human being. Used commonly by God when addressing mortals to remind them of their place in the general scheme of things. (And used commonly in modern Hebrew to indicate that someone is a regular chap, he's a "ben adam". 'Don't be so hard-nosed, be a "ben adam"!')
The everlasting dominion given to the "ben adam" (by inference the Seleuicids were not that) is the House of David that will be re-established, and this time permanently, as promised by previous prophets. The messiah is a human king, who gets married and hopefully has righteous kids, one of whom continues the line after his death.
As time went by and the House of David looked less and less likely to return, the concept of messiah took on ever more mystical overtones and lent itself to speculative excesses. In light of the bad experiences with various claimants to the title over the generations, the Rabbis now take a dim view of any speculation concerning the nature of the messiah and his estimated time of arrival. Among non-religious Jews today, particularly those on the left of the political spectrum in Israel, "messianic" is an epithet used to infer that someone on the other side of the spectrum is backward, dangerous, reactionary, etc.