A phrase first brought to public attention by T.S. Eliot in his 1919 essay on Hamlet. It refers to a literary description (or a sequence in a play) that depicts a emotion, and hopefully evokes that emotion in the reader (or viewer).
Eliot said that if we are to believe in the emotion characters are showing in a work of art, that emotion must relate to, and be in scale with, the situation put forth in that work of art. If the emotions shown are too melodramatic or too phlegmatic for the setting, it looks unconvincing.
My favorite example is Who's on first?, which while not the most literary of examples, is an excellent case of getting the audience to feel empathy with the character. (I only empathize with Costello. Maybe someone out there feels for Abbot.) Every time they start the cycle again, you know exactly what Costello is going through, and his reactions are perfect. On the other hand, I suspect that T.S. Eliot would not think that this was a well-done objective correlative, as it is (just slightly) exaggerated for the sake of comedy. To each his own.