"The goat became very great, but at the height of its power his large horn was broken off, and in its place four prominent horns grew up toward the four winds of heaven" NIV translation
The Greco-Macedonian empire grew to dominate the known world including defeating the Media-Persian empire. Alexander had greater ambitions of moving further east but his army refused after eight long years of battle. They returned to Babylon which was going to be the capitol of his empire. After a drunken party, Alexander became sick and died ten days later probably due to poisoning. His empire was divided into four parts by his generals.
"Out of one of them came another horn, which started small but grew in power to the south and to the east and toward the Beautiful Land. It grew until it reached the host of the heavens, and it threw some of the starry host down to the earth and trampled on them. It set itself up to be as great as the Prince of the host, it took away the daily sacrifice from him, and the place of his sanctuary was brought low. Because of rebellion, the host of the saints and the daily sacrifice were given over to it. It prospered in everything it did, and truth was thrown to the ground." NIV translation
The horn refers to Seleucus one of the generals that took a part of Alexander's empire. And in his line came Antiochus IV Epiphanes who would become the king of the Seleucid Empire. They would rule over Israel and even the city of Jerusalem.
The rest of the passage describes the desecration of the temple that happened under his reign. The passage also speaks of the coming Anti-Christ who will also set himself up to replace God.
"Then I heard a holy one speaking, and another holy one said to him, 'How long will it take for the vision concerning the daily sacrifice, the rebellion that causes desolation, and the surrender of the sanctuary and of the host that will be trampled underfoot?' He said to me, 'It will take 2,300 evenings and mornings; then the sanctuary will be reconsecrated.'" NIV translation
There have been many attempts to explain this prophecy and its relation to future end time events. To rightly understand this passage, we must remember that this portion (unlike the part before it) of the Book of Daniel was written in Hebrew instead of Aramaic. The Jewish day begins with the evening due to the description of a day in Genesis 1:5. We can therefore know that this is speaking about the fact that the desolation of the temple would last for 2300 Jewish days. The temple was cleansed on December 25, 165 B.C. and if we count back we see that the desolation and persecution under Antiochus began at this time. 2300 days is about seven years and that corresponds to the Great Tribulation of Revelation. Although Daniel's vision does not give us any clue about the day that Jesus will return, it does show us the truth of the length of the Great Tribulation.