Broadly, any infringement of copyright by copying, or copyright-related theft.
Despite the images it may evoke of ocean-going bearded villains with swords, when it comes to copyright law, piracy is a catch-all term, used to describe many different sorts of copyright infringement, and all types of illegal copying.
Some analysts have pointed to and criticized a semantic trend from using piracy to describe only large-scale copying for commercial gain to using, to describe any unauthorized of copying.
But, the fact remains that common usage uses the term piracy to describe not only organizations making hundreds of thousands of counterfeit DVDs, but also to describe peer-to-peer file sharing and at-home, individual personal copying, which may or may not be fair use, depending on who is doing the analysis.
The content industry sees illegal copying as a very serious threat, which may account for their routine usage of such a loaded word, perhaps in an attempt to impute the traits of the very worst sorts of copying to all of it.