And it waxed great, even to the host of heaven; and some of the host and of the stars it cast down to the ground, and trampled upon them. (ASV)
This is the context for this verse.
1 In the third year of the reign of king Belshazzar a vision appeared unto me...Daniel...
2 And I saw in the vision; now it was so, that...I was in Shushan the palace,...and I saw in the vision,...
3 ...behold, there stood before the river a ram which had two horns:
5 And as I was considering, behold, a he-goat came from the west over the face of the whole earth, and touched not the ground: and the goat had a notable horn between his eyes.
8 And the he-goat magnified himself exceedingly: and when he was strong, the great horn was broken; and instead of it there came up four notable horns toward the four winds of heaven.
9 And out of one of them came forth a little horn, which waxed exceeding great, toward the south, and toward the east, and toward the glorious land.
10 And it waxed great, even to the host of heaven; and some of the host and of the stars it cast down to the ground, and trampled upon them.
Daniel 8:2-14 describes a vision; the elements of this vision are explicitly described as being symbolic rather than literal, physical elements in Daniel 8:14-27. Rank literalism is most inadequate as a hermeneutical key to illumine this apocalyptic narrative! Within the context of the passage, it is obvious that the "host of heaven and stars" does not refer to literal, physical stars. We do not understand the passage to be saying that a literal, physical horn growing out of a literal, physical he-goat grabs the stars and cast them to the ground. Even common sense tells the reader that the elements are allegorical and represent something other than a literal, physical horn, a he-goat and stars.
SUM: Daniel was no literalist; he considered the symbols of this vision very difficult to interpret properly (Dan 8:23). The Pro section above presumes but does not demonstrate that the 8:10 was intended literally. This is a very precarious and quite indefensible presumption to make when interpreting apocalyptic literature, especially since the text itself makes it quite plain that almost everything in it is symbolic.
Some identify the meaning of the allegorical elements in this way:
The great horn of the male goat in 8:8 is specifically affirmed in the text as symbolic of Greece (i.e. Alexander the Great) according to 8:21. The four horns which grew when this one was shattered are symbolic of four kingdoms (i.e. the four divisions of Alexander's Empire by his four Generals). From one of these four horns would come a "little horn" (8:9) which would grow great "toward the south, toward the east, and toward the Glorious Land" (Dan 8:9b). Judea, the "Glorious land," was annexed to Egypt under Ptolemy I after a period of debate (finalized 320BC). Although Judea was now under the rule of a Ptolemaic/Egyptian imperial governor (to continue until 198BC), and had to pay taxes, it remained to a large extent politically autonomous. Jerusalem itself (including an area extending a few miles from the city) continued to be ruled according to the laws of the Pentateuch administrated by a succession of hight priests. "The Scepter" (Gen 49:10) had not yet departed from Judah. In 198BC, the Selucids gained control over Judea after their win at Paneion (Caesarea Philippi) after a bitter struggle with the Ptolmies. Judea, now under Selucid control, continued to enjoy political autonomy, however a vigorous campaign by the Selucids to "civilize" the Jews (i. e. Hellenize, encourage adoption of Greek language and culture) polarized the Jews into factions (The Hasidean ("the Pious") faction resisted hellenization; others, including priests, capitulated). In 190BC with Rome's defeat of the Selucids (Antiochus the Great of Syria) at the battle of Magnesia, the Selucids lost territory and were forced to pay enormous tribute, a burden which had to be born in part by Judeans (many subsequent events in biblical history are strongly related to this heavy economic burden). The fate of Judea, which had been semi-autonomous under the Selucids, was now in Roman hands. In 175-163BC Selucid King Antiochus IV Epiphanes (Epiphanes literally means "the manifest God") reigned in Judea. (cf. "He even exalted himself as high as the Prince of the host; and by him the daily sacrifices were taken away, and the place of his sanctuary was cast down" -Dan 8:11). In 167-164BC Antiochus Epiphanes outlawed Jewish religion in reaction to the ousting of Menelaus (the puppet hellenizer high priest Antiochus installed to replace Jason). This act infuriated Antiochus; he considered it an act of open rebellion against his rule, and he retaliated mercilessly. Sabbath observance and circumcision were outlawed, the death penalty was proclaimed for possession of the Hebrew Scriptures and for circumcision (cf. 1 Macc 1:48ff.). The Temple was converted into a Zeus cult, its treasury looted, and a Hellenistic constitution was established. This resulted in the Maccabean revolt, which is beyond the present scope. Antiochus was fiercely determined to convert or exterminate all resistance to forced hellenization in his domain (i.e. cultural genocide of the Jews and their God).
In apocalyptic terms, such a move was not just a move against an historic people (the Jews), but against the "heavenly host" (Dan 8:10) herself (the Jews were, as the people of God, themselves conceived by the Hebrews to form a part of Yahweh's hosts). It is virtually inconceivable that in an apocalyptic vision such as this came a sudden literalistic turn requiring the reader to consider the fall to earth of the red giants and white dwarfs we see in our telescopes to be trampled by the fleshly feet of Antiochus IV along with Jews of his day. Crass, uncritical literalism most certainly is not the proper key to unlock this apocalyptic door!
Edit this section to note miscellaneous facts.