The Idea in Brief
The Jewish (and pre-Christian) understanding of the abomination of desolation was the desecration of the Jewish temple reconstructed by Zerubbabel. The abomination of desolation (or, with more literalness: the abomination of what precipitates the vacating [of holiness]) had the primary Jewish understanding through Antiochus IV Epiphanes, who had desecrated the Jewish Temple through idolatry in 168 BCE. The secondary meaning had to do with the desecration of idolatry at Sinai, when the Jewish people substituted the place of Yahweh with the golden calf. That is, both of these desecrating events through idolatry had occurred on the same date in Jewish history.
Tractate Ta‘anit of the Babylonian Talmud deals with the general areas of repentance and penitence relating to divine discipline with an emphasis on fasting. In this tractate there appears several unfortunate events in the history of the Jewish peoples which have immediate relevance to the discussion at hand. For example, the several verses in Daniel regarding the "abomination of desolation" appear to correlate with the same date in Jewish history when Moses destroyed the tablets upon seeing the golden calf of idolatry. That is, this very same date in Jewish history was the public burning of the Torah by Antiochus IV Epiphanes, who then desecrated the Temple with profane sacrifices and the great image of idolatry. The following citation is the relevant portion taken from the English translation of the Babylonian Talmud by Jacob Neusner (2011), Tractate Ta'anite 4:1, XIII-XVII [Folio 28B and Folio 29A] - please click the image to enlarge.
The mention here of "Apostomus" appears to be Antiochus IV Epiphanes. That is, the abomination included both the desecration of the Torah and Temple, in which Antiochus IV Epiphanes erected the infamous idol. These observations in the Gemarah of the Talmud comprise the first line commentary on the Mishnah (which is the core of the Talmud), and therefore carry gravitas on the Jewish (and pre-Christian) understanding of the meaning of "abomination of desolation."
The abomination of desolation (or, in colloquial contemporary English, the abomination which wipes out what is holy) appears to relate to idolatry, which displaces Yahweh as the object of divine worship. That is, Jewish oral tradition (as found in the Babylonian Talmud) correlates the date of the desecration of the Zerubbabel's Temple through idolatry by Antiochus IV Epiphanes in 168 BCE with the date that the Exodus generation had substituted the worship of Yahweh with the golden calf of idolatry.
Neusner, Jacob (2011). The Babylonian Talmud: A Translation and Commentary (Vol. 7a). Peabody, MA: Hendrickson Publishers, 154-155.