The vision in 8:3-14 concerns a ram and a male goat with its successors.
Verses 3 and 4 speak of a ram.
The ram signifies Medo-Persia (vv. 3a, 20; 11:2).
The ram was standing before the river (8:3b). This signifies that the ram became strong by the river Ulai.
The ram had two horns, and "the two horns were high, but one was higher than the other; and the higher one came up last" (v. 3c). These two horns signify Media and Persia. Persia with its king Cyrus (Ezra 1:1), which came up last, became higher than Media.
Daniel saw the ram pushing westward, northward, and southward (Dan. 8:4a). This signifies that Medo-Persia conquered Babylon on the west, Assyria on the north, and Egypt on the south.
"No beast could stand before him, and there was no one who could deliver from his power" (v. 4b). This signifies Medo-Persia's subduing power.
"He did as he pleased, and he became great" (v. 4c). This indicates that Medo-Persia had no fear of God and became arrogant in itself. Eventually, God dealt with Medo-Persia by raising up Alexander the Great.