Antigone and Ismene are the daughters of Oedipus and have been living under the protection of their uncle, Creon, king of Thebes. We are re-introduced to these characters, just mentioned in Oedipus Rex, in Antigone by Sophocles.
At the beginning of the play, Antigone is outraged at what the king has done. Ismene has heard nothing about it, so Antigone tells Ismene about Creon's decree:
Creon buried our brother, Eteocles, with military honors, gave him a soldier's funeral, and it was right that he should--but Polyneices, who fought as bravely and died as miserably--they say that Creon has sworn no one shall bury him, no one mourn for him, but his body must lie in the fields, a sweet treasure for carrion birds to find as they search for food. That is what they say, and our good Creon is coming here to announce it publicly; and the penalty--stoning to death in the public square!
The reason Creon gives Eteocles a proper and honorable funeral and condemns Polyneices to be unburied and unmourned, food for the flesh-eating creatures of the field, is that Polyneices died fighting against his own brother and and against Thebes. Creon wants to re-establish order after such a battle, and this is his edict for his nephews.
Antigone believes that every person deserves a proper burial, mo matter their deeds in life, for the belief of the day was that the soul of an unconsecrated body was condemned to wander the world for a hundred years. Both of her brothers fought bravely, and Polyneices had some justification to seek revenge against his brother and his uncle. Even if those things were not true, however, Antigone would still have insisted on a proper burial.
Antigone adds, "There it is, and now you can prove what you are: a true sister, or a traitor to your family." Ismene is too afraid to go against her uncle, tradition, and the law; she says they are just women and should be obedient to the men who are in power. Of course Antigone is even more determined to act when she hears what her sister says.
If that is what you think, then I should not want you, even if you asked to come. You have made your choice; you can be what you want to be. But I will bury him, and if I must die, I say that this crime is holy. I shall lie down with him in death, and I shall be as dear to him as he to me. It is the dead, not the living, who make the
greatest demands: we die forever....
The line you mention in your question is found in this speech to Ismene. Antigone intends to give Polyneices a proper burial, even outside of the city walls, and she is willing to pay the price, which is her life, if she must.
When Antigone calls what she is about to do (and eventually does) a "holy" crime, she means that it is something which breaks man's laws (thus, a crime) but which adheres to God's laws (thus, it is holy). One of the grand themes of this play is this question: which law is supreme, the law of God or the law of man? Antigone, by her words and deeds, clearly believes it is her holy and sacred duty to take ensure her brother's soul is at peace, even if she must commit a crime against the state to do so.