Background
The prophet Daniel was given strange dreams and visions during the first year that Belshazzar ruled over Babylon. The first three of the animals he saw was one like a lion, the second like a bear, and the third like a leopard (Daniel 7:1 - 6). These represented the kingdoms of Babylon, Medo-Persia and Greece (Alexander the Great). These empires were also symbolized by the great image of a man seen by Nebuchadnezzar (Daniel 2).
Why Beasts?
God uses certain animals, in part, to represent humanly created kingdoms because they share some general traits.
Creatures such as lions and bears use their strength, cunning and agility to hunt their prey. They can attack without warning at a time and place of their own choosing. The purpose of their behavior is to forcibly and violently take the lives of other beasts for their own purposes (food). These animals are vicious killers without mercy or concern for how their actions affect others.
Human-led kingdoms such as those of Babylon, Persia and Greece used violence to overcome nations and peoples. They viciously attacked innocent humans, usually without warning, so that they could fulfill their own selfish goals. They had little if any concern for those they dominated. They, without consent, usually harshly ruled those who they did not kill.
Lions
Lions are mentioned 150 times in the King James Bible. They are considered an apex predatory of land animals (Job 38:39) and the king of beasts. Lions are stated to possess strength and power (Proverbs 30:30), boldness (2Samuel 17:10), ferocity (Psalm 7:2), and stealth (Psalm 10:9; Lamentations 3:10).
King Nebuchadnezzar, the greatest ruler over the Neo-Babylonian kingdom, is represented by a lion in Daniel's vision (Daniel 7:4). As lions are considered the greatest of all beasts, Nebuchadnezzar is labeled by God "a king of kings" (Daniel 2:37) and Babylon "the glory of kingdoms" (Isaiah 13:19). He possessed power, strength and glory (Daniel 2:37). Like an animal, however, he also indulged in violence and cared little how his actions affected others (4:27).
Bears
Bears, another animal that can be vicious, are known for their formidable strength and violence (1Samuel 17:34, Amos 5:19; Hosea 13:8). They attack those who are helpless against their power (Proverbs 28:15). They represent the Medo-Persian Empire (Daniel 7:5) which was both strong and fierce. The Persians were known for their violent attacks and gruesome acts, desiring the spilling of blood above gold or silver (Isaiah 13:15 - 18). They were likely the creators of using crucifixion as a long and excruciatingly painful means of killing their enemies.
Leopards
Leopards are known for being cunning animals. They are willing to watch and wait for the right time to attack their prey (Jeremiah 5:6, Hosea 13:7). They are also known for being swift and formidable killers (Habakkuk 1:8). Leopards, in Daniel's dream, represent the Macedonian (Greek) empire of Alexander the Great (Daniel 7:6).
Alexander's cunning and swiftness, like an animal, enabled him to go undefeated on the battlefield even though his enemies usually outnumbered him. His ability to stealthy and rapidly ambush his foes is legendary. In the incredibly short span of 10 years (336 to 326 B.C.), Alexander conquered territory stretching from Greece to as far south as Egypt and as far east as northwestern India. In a mere decade, he took control of roughly 2 million square miles (about 5.2 million square kilometers) of land!
Dragons
Dragons are found thirteen times in Revelation (12:3 - 17, 13:2 - 11, 16:13 and 20:2) and 35 times total in the King James Bible. Thirteen is highly symbolic as the number represents rebellion and lawlessness.
The Bible states this animal is venomous (Deuteronomy 32:33), as dangerous as a lion or adder (Psalm 91:13) and possesses the ability to swallow up their prey (Jeremiah 51:34). They are wild, solitary and untamable animals that roam desolate places like wildernesses (Job 30:29, Isaiah 13:22, 34:13, Jeremiah 9:11, 10:22, Malachi 1:3). They are also full of vanity (Ezekiel 29:3).
The Great Spiritual Dragon
Like a dragon, Scripture states Satan the devil is a restless being who roams the earth (Job 1:7, 2:2). He is like an untamable vicious animal who attacks anyone he can so that he can destroy them (1Peter 5:8). The devil is also full of vanity and self-centered lusts (Ezekiel 28:17, Isaiah 14:13 - 14, John 8:44).
The devil will soon be manifested to the entire world through the Beast and False Prophet. Through them he will establish a worldwide kingdom aptly named Babylon (Revelation 14:8, 17:5,). Like a vicious animal he will seek to fulfill his will without mercy or pity. One of his first tasks will be to hunt down and destroy any Christians he can find (Revelation 12:17, 13:7). He will also, like a cunning serpent, deceive the world into receiving a mark and worshipping him (13:15 - 17). His grip over humanity (Revelation 13:4), however, will end with Jesus' Second Coming (Revelation 19).