As other posts here indicate, "artificial" in the 1600s would mean created by humans. The Leviathan represents political power or the commonwealth, which is made up of the many parts of the social order.

Hobbes' influential text, which expresses an early and important theory of the social contract, does not suggest power—especially the absolute power of a monarchy such as he favored—derived from nature. Unlike medieval ideas of nobility or gentility, which suggested that the people who were noble were of an originally better type, Hobbes denies a natural or genetic quality to power. Similarly, unlike Stuart monarchs, Hobbes denies a metaphysical or divine source of monarchy. The monarch is not more like the divine than any other person.

Instead, the absolute sovereign is powerful because the people trade their right to self-rule in order to gain greater security. It is a contract that the people of the commonwealth willingly enter in to and thus is artificial, or made by humans.

The answer to this can be found in the very first paragraph of the introduction to this work.  There, Hobbes argues that the leviathan is artificial because it is made by people to imitate something in nature.

Hobbes argues that anything that people make to imitate nature is, by definition, artificial.  He says that the leviathan is artificial because it is made by people to try to imitate a human being.  He then goes on to list various parts of the leviathan and to note which parts of the human being they correspond to.  As a couple of examples, he says that the sovereignty of the leviathan is its soul and the laws are the will of the being.  There are also more physical parts, such as the government officials, who are the joints of the being.

Because the leviathan is made by human beings in this way, it is an artifical human being on a very large scale.