What is the definition of objective correlative?
Concerning "objective correlative," since you specifically ask for a definition, I'll quote one from a handbook:
...an external equivalent for an internal state of mind: thus any object, scene, event, or situation that may be said to stand for or evoke a given mood or emotion, as opposed to a direct subjective expression of it.
That's from an Oxford dictionary of literary terms. In other words, an objective correlative is something that comes to represent a state of mind or mood or emotion. It raises that emotion in the reader. An old, tattered coat, for instance, which signals a character's poverty, can evoke pity. Instead of a direct statement that suggests a reader should feel pity for a character, a writer uses the coat to do the work.
In T.S. Eliot's own words (he popularized the concept in a 1919 essay), an objective correlative is:
...a set of objects, a situation, a chain of events which shall be the formula of that particular emotion [the emotion the writer wants to create in the reader]; such that when the external facts, which must terminate in sensory experience, are given, the emotion is immediately evoked.
Eliot faulted Shakespeare's Hamlet, calling it an artistic failure, because, he wrote, the external facts of Hamlet's situation, do not fit the mental state he exhibits throughout the play.
One final definition for you, from enotes:
An objective correlative is a literary term referring to a symbolic article used to provide explicit, rather than implicit, access to such traditionally inexplicable concepts as emotion or colour.