The author of this article explains the phenomenon perfectly:
"All the elements of a great mansplaining were in place: painting oneself as a brave truth-teller in the face of scolding feminist mommies, declaring yourself the authority on women’s feelings, arguing that women’s main and possibly sole motivating force is male attention, and assuming that the world is deeply interested in your aesthetic opinions about ladykind."
According to this article, the word "mansplain" originated in an article by Rebecca Solnit, whose 2008 essay “Men Explain Things to Me”told the painfully hilarious story of when she was talking to a man who, assuming she knew less than he did about everything (because, hello, she is a woman), began to tell her all about a book which she had authored.
Check out this Tumblir page for a few examples of mansplaining in academia: "Academic Men Explain Things to Me."
Unfortunately, the word "mansplain" has lately been applied to situations where it doesn't quite explain what's happening.
Unfortunately, also, its use has turned into another weapon in the gender wars. As if we needed another one.