Intertextuality is the influence that a literary text has upon other literary texts. Nearly every literary work relies on what was written before, and draws parallels, whether in structural or some other sense (such as topics, characters, messages, etc.). Generally, it means that all the literature is a giant web of references, influences, shared themes and values, and that nobody can learn to be original without having dealt with thousands of other authors' works.
For example, Vergil's Aeneid was heavily influenced by Homer's Iliad. In a way, it is a sequel of some of the occurrences from the Iliad - although it is artistically independent and has an immense value in its own right. We even meet some of the Iliad's heroes there - such as Achilles, who is now in the Underworld, long dead and regretting that he didn't live longer. We cannot get the whole picture about Achilles from Aeneid (nor understand the context of his suffering) if we didn't read the Iliad first and see him there, in his full glory.
The second example would be Dante's Inferno. Although it was written in the 14th century, it deals and debates with nearly every literary work from antiquity. There are many heroes from Iliad and Odyssey (including Odysseus himself) - and there is Virgil, the Aeneid's poet, who is Dante's tutor and protector on his way through the underworld. Dante refers to Aeneas as a man who has been to the underworld.
The third example would be Joyce's 20th-century novel Ulysses. It is a giant monument to intertextuality, as it depicts a one-day journey of Leopold Bloom, which corresponds to Odysseus' wandering on his way home to Ithaca. Just like Odysseus has his Penelope, Leopold has his Molly Bloom. The novel is structured in episodes which all resemble corresponding occurrences in Odyssey. Of course, one can read Ulysses without being familiar with the Odyssey; but a great layer of meaning and significance would be lost.
