The interpretation of Daniel 8 is easier than that of some other chapters, since the identification of the two main animals are given explicitly:
As for the ram that you saw with the two horns, these are the kings of Media and Persia. And the goat is the king of Greece.
(Daniel 8:20-21)
Thus, the chapter is only hard to understand because most people don't know this period of history very well. But we can connect most of the details to historical events.
Daniel sees the ram “charging westward and northward and southward”. This refers to Cyrus the Great's campaigns:
West – against the Lydian empire in Turkey (the Battle of Thymbra in 547 BC)
North – against the Massagetae in central Asia
South – against the Babylonian empire (the Battle of Opis in 539 BC)
The horn of the goat (verse 5) is Alexander the Great, who died in 323 BC. In eight years Alexander had conquered everything between Greece and India. This speed is reflected in the fact that the goat moves “without touching the ground”.
In verse 7, the goat knocks the ram down and tramples on him. This refers to the defeat of the Persians in the Battle of Issus in 333 BC, when Alexander defeated Darius III. This is depicted in the famous “Alexander Mosaic” found in Pompeii.
After his death, Alexander's empire was divided between his four generals: Cassander (who got Macedonia), Lysimachus (Thrace), Seleucus (Syria) and Ptolemy (Egypt). These are the four horns of verse 8:
As for the horn that was broken, in place of which four others arose, four kingdoms shall arise from his nation, but not with his power.
(Daniel 8:22)
Verse 9 says that out of one of these horns, a little horn will arise. This is talking about Antiochus IV Epiphanes, who ruled the Seleucid Empire in Syria from 175 to 164 BC. He took the title “Theos Epiphanes”, which means “God Manifest”. Hence the comment in verse 25 that “in his own mind he shall become great”.
This little horn “grew exceedingly great toward the south, toward the east, and toward the glorious land” (verse 9). These statements refer to Antiochus' military campaigns: against Egypt in 169 BC (further described in Daniel 11:25-30) and against Parthia in 166 BC. He also persecuted the Jews, which is the focus of Antiochus' place in the Book of Daniel.
Contrary to his predecessors' policy of tolerating Jewish worship, Anthiochus IV outlawed it. This story is told in the books of 1 and 2 Maccabees, in the Apocrypha. Antiochus ordered that the Jews worship Zeus, and then slaughtered them when they refused. In 168 BC, he desecrated the Temple by sacrificing a pig on the altar of incense and setting up an idol. (This is the “abomination that makes desolate” in Daniel 11:31, but not, I think, what is talked about in Daniel 9:27.) Antiochus' actions led to the Maccabean revolt, led by Judas Maccabeus, and the rededication of the temple in 165 BC. This is event commemorated in the Jewish celebration of Hanukkah, which Jesus also observed in John 10:22-23 (where it is called the “Feast of Dedication”).
Antiochus IV died suddenly of disease in 164 BC, an event prophesied in verse 25: “he shall be broken—but by no human hand.”
In conclusion, this history is important for us to know as it forms a vital part of the background to understanding God's Word. It is also part of the history of God's people – we can think of the Maccabean period as a kind of “Old Testament Church History”. So even though it is rarely taught in schools, this is material that Christian parents should pass on to their children.