The poem uses a number of metaphors to illustrate the leader's power—which is primarily a destructive power.
For example, the speaker repeatedly compares the leader's "hand" or individual "fingers" to powerful rulers in their own right. Line 2 refers to the leader's "five sovereign fingers," later rephrased as "five kings" (lines 4 and 13). The speaker claims that these five miniature "kings," through the act of signing a treaty, caused the death of a real-life ruler (perhaps a literal "king"). The metaphor "These five kings did a king to death" suggests, then, that the treaty-signing leader holds more power in just one finger than the sovereign leader of another nation.
The leader's "mighty," king-like hand is also said to have "taxed the breath" and "Doubled the globe of dead." These metaphors also stress the leader's deadly power, which took away (figuratively, "taxed") the breath of life from many people—so many that the total number of corpses in the world "Doubled." ("The globe of dead" might refer more specifically to some underworld or afterlife, whose population the leader's policy has doubled. Regardless, the meaning is the same: even accounting for hyperbole, the leader has caused genocidal levels of death.)
Finally, line 15 (a simile rather than a metaphor) draws a pointed, ironic comparison:
A hand rules pity as a hand rules heaven;
In context, this means that the leader subdues their compassion (i.e., for their victims) as strictly as the hand of God rules over heaven. Yet the leader's emotional repression has clearly resulted in the opposite of "heaven": it's created a hell on earth.