Intertextuality comes from our daily conversations. It is something we do, when we talk to each other: we pick up words from each other to create a coherent dialogue. I call this echoing.Written texts can also refer to each other by using links like a hypertext. I call this quoting. Sometimes we mock each others' voice, its tone, its pitch etc. and we get parody. Sometimes we talk about other groups who are not present and we try to imitate their dialect. Then we do pastiche. If we put on a wig or a mustache to imitate someone from the other sex, we do travesty, possibly, also using gestures to match the tone of the female or male person we are imitating. In carnival all three of these practices occur together. Between written or printed texts, practices change. And they change again with films that carry tracks for sounds, music, and images.
All this falls under intertextuality, and its theory, grounded in dialogue, goes back to Russian formalist Mikhail Bakhtin. Since the 1930s the theory has undergone some major changes. It has played a role in creating poststructuralism and it is still an exciting area of research. See Readings (above) for some important theories.
Maybe it is best to start with echoing.