The beast had four heads. This signifies that the four wings for swiftness became four heads, four generals who became the heads of four kingdoms. After the death of Alexander the Great, his four generals divided his empire into four kingdoms.
The third beast was given dominion. This signifies that it was given authority to rule over the nations.
The fourth beast (7:7-8) is the beast as revealed in Revelation 13:1-2.
The fourth beast corresponds to the legs of iron and the feet partly of iron and partly of clay of the great human image in 2:40-43, signifying the Roman Empire.
As signified by iron, the fourth beast was dreadful and frightful and exceedingly strong.
This beast had large iron teeth and claws of bronze, and it devoured, crushed, and trampled under the remainder (v. 19). This signifies that it had great power to devour and crush nations and trample down the remainder.