I take this definition of midrash from Rabbi Lawrence Kushner in his book, “God Was in this Place and I, I Didn’t Even Know”:

What might have happened before and after, above and below the biblical story. Imagine, for instance, that your life, as it superficially appears to others, is the apparent text. Beneath and within you move forces and fantasies-often concealed from those watching and even from yourself-that are the matrix for each outward event. In a similar way, midrash attempts to “imagine” how the apparently discordant “words” of the text might be woven into a larger coherent whole. Such an approach is more than literay criticism. Only when the words of the text are holy, or, like a love letter, are read with a diligence of attention bordering on reverence, can midrash occur.