Intertextuality is the practice or method of defining the meaning of a text by its relation, similarity, difference, connection, etc. with other texts. It is Julia Kristeva’s term (originally) as the logical analogue of Saussure’s concept of meaning in words (signs).
Saussure stated that all words derive their meaning from their difference/similarity to other words. This means that the word “Tree” has no essential relation to the actual tree or the concept of tree. The choice of T-R-E-E is arbitrary. Case in point, in German, tree is B-A-U-M. The construction of words for things and concepts is cultural/socially constructed; (made up by humans). There is nothing about the nature or metaphysicality of the tree concept that necessitates it being spelled T-R-E-E. So, the word “tree” gets its meaning, not from the word itself, but how it INTERRELATES with other words. A “tree" is a “plant” that “breathes” and has “bark.” You need other words in order to define tree. The same goes for the actual tree and the concept of tree. The real tree exists because of other factors interrelating with itself; dirt, CO2, sunlight, etc. The concept tree is also meaningless by itself. You can’t describe a tree (to someone who doesn’t know what a tree is) simply by saying “a tree is a tree.” You have to relate it to other concepts.
Intertextuality is the method of employing this to literary texts. A single text is defined by how it interrelates with other texts. It liberates the meaning of a text from the limitations of authorial intent, historical background and historical context. Overall, its strengths outweigh its weaknesses.
One weakness is that the term “intertextuality” is so all-encompassing that it obscures more nuanced forms of literary analysis. For example, a parody is a kind of intertextuality because it mockingly refers to another text(s). Or, a text could interrelate with music, art and the ways intertextuality works become more complex and cannot be defined by intertextuality, because at further levels of complexity and interdisciplinarity (which is the interrelations of different subjects – music and math for instance) the concept of intertextuality is an oversimplification. It would be obvious to simply say that “everything relates to everything.” You have to go further than that and in more specific analyses, you have to answer the ‘so what’ question. Everything relates to everything. So what? How is that relevant in this (any specific study) situation?
The big weakness, which is a strength as well, is the infiniteness of intertextuality. If any text can relate to any text, ad infinitum, then meaning is endlessly deferred or, it is never complete. This endless wandering is liberating but when it comes to applying real social, human meaning, it can obscure practical applications of meaning such as political, authorial or historical. Example: if you have a text in which one meaning is a strong political statement that is intended to be a source of liberation for an oppressed group, and the meaning becomes entangled in an endless series of intertextual tangents, it loses its real life socio-historical applicability = it loses its significance and individuality.
Intertextuality is a basic property of literature and meaning, but for practical and real life purposes, it must be contained and guided, a give and take, as if you were steering a sailboat through an endless sea of meaning.