Simply, Antigone defied Creon's decree of Polynices, her brother, of not having a proper burial but she instead gave him one. In those days, the Greeks believed that proper burial should be given so that they could have a chance to enter to the afterlife.
As Polynices fought Eteocles in their fight for leadership in Thebes, the kingdom and its peace was destroyed. Thus, Creon, the King, declared for Polynices not to be buried because he ruined the city.
She was arrested also because she confessed to the crime, without hesistation, thus leading to her persecution.