As king, Creon decrees that son of the former king, rebel Polynices, shall not be buried and shall rot in the open as an example to others that would think of taking action against the state. Anyone attempting to bury Polynices would be killed for actions amounting to a collaboration with the dead rebel.
This decree is severe in many ways. Polynices' brother, Eteocles, had assumed the throne of Thebes according to the rule set down by Oedipus (former king of Thebes and father to Polynices, Eteocles and Antigone). Eteocles goes against the rule of Oedipus, however, when he refuses to step down from the throne at the appointed time so that Polynices could take his turn as ruler of Thebes.
Polynices then had a legitimate reason to defy the rule of Eteocles (Polynices was supposed to be the one on the throne). Why is this important?
When Creon identifies Polynices as a dishonorable man, he is doing so according to the strictest possible letter of the law. He is choosing to defend the integrity of the state by adopting a very unforgiving and narrow view of what actions might constitute rebellion or insurgency. He extends this rather extreme particularity of perspective when he says that anyone sympathizing publicly with Polynices will be killed.
In the action of the play, Antigone does sympathize with her brother Polynices and so stands opposed to Creon's decree.
Creon's reasons for upholding the letter of the law go beyond his concern for the integrity of the state. When he assumes the rule of Thebes, he becomes concerned for his own authority and wants to ensure that his commands, as king, should not be questioned.
"Although he gives lip service to the necessity for order and for obedience to the law, he is a tyrant who has identified the welfare of the state with his own self-interest and self-will" (eNotes).
The political concerns for his own power stand in stark contrast to Antigone's quite human and self-sacrificing concerns for honoring her dead brother with burial. Creon's worry is displayed early on as paranoia. He believes that there are "[s]tiff- necked anarchists, putting their heads together/scheming against [him] in alleys." Creon fumes at his sentry and later at Tiresias, expressing a belief that his power is being undermined.
The extremity of Creon's decree cannot be separated from his insecurity vis a vis his new position as king of Thebes. In acting against a very strict definition of rebellion, Creon is protecting his own authority and pro-actively defending himself against any challenges to his rule.