It's when a man explains something, particularly to a woman or group of women, in a patronising or unnecessary way.
There was a hilarious example in the Christmas Edition of Sherlock when the great man himself gave a short lecture on women's rights while standing in front of...a women's rights group.
It's terrific at last to have a word for such an established custom because now many unarticulated frustrations can be easily expressed.
I wish they'd put the word together with a bit more care, though: after all, it's not as if explain is any sort of divorce negotiation, is it?
Sunday Rest: mansplain. The trigger for the word's coining seems to have been a 2008 post on LiveJournal by Rebecca Solnit, though she didn't come up with the word. A month later, though, it was being used all over the place, and has now even got into the Oxford Dictionary.
As far the word's derivation goes, the plain bit of explain comes from the Latin plānus, which means level.