Mansplaining is a neologism which refers to the patronizing way that certain men tend to explain things to women. Every woman has encountered this at some point in her life -- in the hardware store, on the phone with the IT guy, or talking to the cable installer. No matter her level of expertise (or his: incompetents are just as likely to mansplain as professionals), the mansplainer will patiently, paternalistically walk her through his explanation as if he is talking to a child. His explanation may be redundant, irrelevant, or downright wrong, but that does not matter to him since his main goal is to appear more knowledgeable than she is.
Mansplaining about feminism is particularly common. If a woman mentions an observation about a woman-centered issue, a mansplainer will inevitably swoop in and enumerate several reasons why she is overreacting, that it isn't at all like she says it is, men have it rough too, and so on.
The common protest (perhaps someone is indignantly typing it into the Blab! box as we speak) is that women, too, can be assholes about their areas of "expertise." This is true; nevertheless, the word "mansplaining" needs to remain gendered. This is because society tends to reward men for emphasizing their knowledge, while women are generally punished for it. In other words, the woman who argues with the IT guy about Linux is perceived as a pushy, know-it-all bitch, while the man who does it is simply, well, explaining. A woman who holds forth with stupid explanations will be shamed and eyerolled right then and there; men, however, will be congratulated and encouraged for being "go-getters."
Related portmanteaux include whitesplaining and straightsplaining, where members of dominant groups try to set minorities straight about minority issues.