Hardcore games are those that are soft on the outside, with a hard, crunchy center.
All kidding aside, my understanding is that a "hardcore game" is one typically enjoyed by those who are "hardcore gamers", i.e. - a game that requires a lot of skill or a steep learning curve. Civilization could probably be considered hardcore because of the time and micromanagement required, whereas most FPS/RTS games tend to require time and/or good reflexes. RPGs tend to require a lot of character investment as well as extensive exploration.
Contrast that to a "casual" game such as Wii Play or Wii Sports where someone unfamiliar with the game can be fully involved in a few minutes.
On the other hand, I wouldn't argue that the majority of games on the Wii are "casual", because SSBB, Mario Galaxy, Zelda, etc. can have significant skill and/or time requirements to complete.
EDIT: Fixed the second paragraph.
