The rabbinical consensus is that the expression refers to the 168 BCE desecration of the Second Temple (Herod's Temple) by the erection of a Zeus statue in its sacred precincts by Antiochus IV Epiphanes (the flashpoint of the Maccabean Revolt). Some rabbis, however, see in it an allusion to Manasseh, who is reported to have set up "a carved image ... in the house of God".
Church Father John Chrysostom understood this to refer to the armies that surrounded Jerusalem and the factions fighting within it which preceded the destruction of the city.
Modern biblical scholarship
See also: Book of Daniel § Dating and content, and Gospel of Mark § Date
The 1 Maccabees usage of the term points to the actions of Antiochus IV Epiphanes in the mid-2nd century BC. Specifically, he set up an altar, probably to Zeus or Baal Shamem, in the Second Temple in Jerusalem and sacrificed swine on it around the year 168 BC. Many modern scholars believe that Daniel 9:27, 11:31 and 12:11 are examples of vaticinium ex eventu (prophecies after the event) relating to Antiochus.