Hardcore mode is an optional mode of play for players who really want to challenge themselves and learn new things in unfamiliar categories. When a player decides to enter hardcore mode, his score will be reset to zero, rating reset to 1500, and he will gain a special "hardcore" icon by his name on scoreboards. Special scoreboards will display the top players playing in hardcore mode.
In short, it's something to choose if you want a greater challenge in the Global challenge, and get compared to other such people in scoring charts.
Hardcore mode is explained here: