Everything you ever wanted to know about midrash ... and less
I have come to using the term "midrash" to describe the "more reading" pages that explain, often with spoilers, our puzzles—on both the cosmic level and/or in terms of the minutiae of individual clues.
A "dictionary definition" of "midrash" reads: the body of homiletic stories told by Jewish rabbinic sages to explain passages in the Hebrew Bible, including Torah (adapted from the start of a wikipedia page, which contains much more information).
A much more nuanced description appears here, in my view almost a midrash for a midrash.
I myself was asked to deliver the midrash at my daughter's bat mitzvah, which was held on June 1, 2002. Click here for a video (9 minutes). Some day, I will create an annotated transcript, but don't hold your breath.