What does King Lear mean when he says that ingratitude is a marble-hearted fiend"?"
In Act I, Scene 4, of Shakespeare's King Lear, the title character has arrived with his large retinue — what we might today call an entourage — of 100 knights and squires at the palace of the Duke of Albany and his wife, Goneril, who is Lear's daughter.
Goneril complains about the conduct of Lear's men,
Men so disorder'd, so debosh'd [debauched], and bold
That this our court, infected with their manners,
Shows like a riotous inn.
She asks her father to send away some of his men and keep only those he actually needs.
Lear, being king, is used to giving orders, not taking them. He expects to be treated like a king — even by his own daughter. He flies into a rage, accusing Goneril of ingratitude:
Ingratitude, thou marble-hearted fiend,
More hideous when thou show'st thee in a child
Than the sea-monster!
Marble is cold and hard. Here, Shakespeare uses metaphor by saying that ingratitude is a cold, hard-hearted fiend. Lear goes on to say that this fiend ingratitude, when it appears in a child (and remember that he's talking about his own child, Goneril) is more hideous than a sea monster.
He's basically saying that the way Goneril is treating him is more hideous than sea monster. This is a pretty sharp and unfair rebuke from a father to a daughter.