A latin phrase meaning "my fault" used mainly by politicians where the action or behavior for which fault is admitted is indefensible and/or inexcusable; the phrase is employed in order to admit fault less bluntly and in a way that is not readily comprehended as such by the general population.
President Clinton eventually abandoned his efforts to explain away or defend his affair with Monica Lewinsky in the White House, and instead, Clinton's attorney issued his Client's "mea culpa" with respect to the affair.
It sort of means 'my bad' but it's more like 'yes this was my fault but I can incorporate Latin phrases into my conversation so I'm still better person than you especially as you're going to have to google this phrase. (NB. Can also be used in a tongue in cheek way by some decent people who don't realise lots of people don't know what they mean). Entered more into the public consciousness following the use of this phrase by Jacob Rees-Mogg MP