Hecuba is the Queen of Troy. After the destruction of Troy, Hecuba is taken prisoner and is taken away to be a slave. Her name is always associated with grief and loss, consequently, she is often depicted as a tragic figure in Greek drama. Note that Hamlet refers to her when he ponders the fact that he can weep at a play about Hecuba, but seems to be incapable of avenging his father's murder. Seeing an actor weep for Hecuba's fate, Hamlet says, "What is he to Hecuba, or Hecuba to him that he should weep for her."
Hecuba (Hecabe in Greek) is the wife of Priam, king of Troy, and the mother of 19 of Priam's 50 sons. Among Hecabe's children are Hector, Paris/Alexander, and Cassandra.
In Homer's Iliad, Hecuba does not frequently appear. She is mentioned in Book 6, where she offers one of her robes to goddess Athena. Hector also makes mention of Hecuba's anticipated grief when Troy falls.
Hecuba also appears in Iliad 24, as Priam tells Hecuba that he is going to the Greek camp to try to give Achilles a ransom in exchange for the return of Hector's corpse. Hecuba tries to persuade her husband not to do this, but Priam's resolve remains unchanged.
Hecuba is also present at the end of the epic and leads the women in lamentation for her dead son Hector:
Hector, far dearest to my heart of all my children, lo, when thou livedst thou wast dear to the gods, and therefore have they had care of thee for all thou art in the doom of death.
After the fall of Troy, sources outside of Homer (see especially Euripides' Hecuba) tell us that Hecuba became the property of Odysseus, who would have taken her back to Ithaca with him as a slave, but Hecuba dies on the voyage not long after they sail from Troy.