Hardcore can be used in the description of a number of genres including:
1) Hardcore Punk as well as its various offshoots and derivatives. It can also be used as an adjective rather than a genre, often to describe a Metalcore/Heavy Metal band that sounds heavier or more “hardcore” than other bands.
2) It's also a genre of electronic music, Hardcore in this context is identified by being harder than the other Electronic Dance Music genres and the songs will have higher bpms, sometimes hardcore in this context can be combined with the genres of Techno, House or Gabba.
4) Happy Hardcore, a much harder style of Techno or House with highly up-tempo bass-lines and very fast beat drum lines, and generally vocals (often female) that will have a "heavier" or more "hardcore" production than the standard "top 40 chart" vocal styles.