Define intertextuality. Discuss three examples that have helped you in reading specific works.

Intertextuality is complex and involves different levels. 
I'll try to simplify it a bit. 

Basically, it is the idea
that no text is independent, that all texts are amalgams or mixtures of texts that have
come before them.  A text may be directly influenced by another text, or may indirectly
use language and ideas that have been previously established by other
texts. 

For instance, the Anglo-Saxon epic
Beowulf is related to what came before it--Greek epics. 
Shakespeare used numerous sources to write Macbeth and
Hamlet that are well documented.  Milton imitates Greek epics in
Paradise Lost.  The romantics drastically reacted to the
neoclassicists and rejected virtually everything the writers who immediately preceeded
them believed--and rejection is a reaction:  it's intertextuality.  The moderns reacted
to the Victorians, the postmoderns to the moderns, and on and on.  No text is
isolated. 

Concerning the second aspect of intertextuality,
any literary work that deals with good and evil, for instance, is dealing with ideas
that have been previously established.  There's a reason why The Lord of the
Rings trilogy seems medieval and somewhat Old Testament-like.  It's been said
that every love story written since Shakespeare owes a debt to his Romeo and
Juliet.  And love stories, of course, did not originate with
Shakespeare. 

At its simplest, intertextuality is evident
everytime a novel is made into a movie.  The novel and the movie are both texts, of a
sort.  Allusions are also simple examples of intertextuality.  As pointed out in my
favorite literature handbook, The Bedford Glossary of Critical and Literary
Terms, when a character on Lost is shown reading an
actual novel, that is an allusion.  It is intertextuality.