Gynocriticism is a branch of feminist literary theory. The particular term was created by Elaine Showalter in an essay titled "Toward a Feminist Poetics" published in The New Feminist Criticism: Essays on Women, Literature and Theory. (Random House, 1988) to describe a subgenre or period within the history of feminist criticism. It is closely allied with French theoretical as opposed to liberal Anglo-Saxon feminism. Rather than being concerned simply with recovery of female texts or remediation of social injustice, it argues for a form of difference ideology grounded in uniquely feminine ways of reading and creating language, which engage female literary works in a manner inaccessible to traditional male types of criticism.
When you write your assigned note on `gynocriticism`, your teacher probably wishes to see you focus on the contrast between this and the liberal feminism which came earlier and more recent gender theory.