Two "beasts" appear in this chapter. It is quite characteristic of apocalyptic visions for animals to symbolize human beings. In this instance, we see (in v.18) that the beast is a man, for he has a "man's number". For many readers, the book of Revelation is dominated by the number "666". And all kinds of attempts have been made to "calculate the number of the beast" to discover his identity, but I think John wants it to remain an enigma. It is beyond the scope of this brief commentary to review some of the more creditable efforts to unravel the mystery.
The important thing to keep in mind is the expectation of a powerful, charismatic leader who will appear on the world stage and dominate it (or "exercise his authority" (v.5) for "forty-two months". For that period of time he has total control "over every tribe, people, language and nation" (v.7). What is more, he has a side-kick who acts on his behalf with awesome signs and wonders (vv.13-15), so effective and intimidating that he is able to "deceive the inhabitants of the earth" (v.14). Why, he can even make a statue of his boss talk!
He also imposes a strict economic policy on the people of the world — so that only those who "receive a mark on their right hand or on their forehead" are able to buy and sell (v.16,17). These two beasts have become known as the "Antichrist" and the "False Prophet".