Playing a Hardcore Character
More details
As stated in the help file, once you reach level 30 with your hardcore character, all your registered / linked characters get + 1 skill point. They will also get +1 more skill point for every 5 levels after 30. This will also apply to any newly created character, as long as they are properly registered and linked. This can offer a nice advantage, especially if you are able to get your hardcore up to a relatively high level.
If you hardcore character dies, you are no longer able to leave town or level up. All of your accumulated skill point bonus remains. If you wipe your hardcore character in order to try again, all accumulated points will be taken away. If one of your other characters has already spent the points, they will not have their skills reduced, but they will have a negative balance of points to spend.
Hardcore characters can not make use of the big red button, and also will get no xp if they join a party banner with a non hardcore character. Because of this they can require more effort to make progress with. One death is final, which can make it harder to work with guilds that have built in mechanics that lead to potential deaths (Mages / Sii etc). Just due to the mechanics of some guilds, they can be seen as better suited for supporting a hardcore, though an experienced player might find opportunities to succeed in any guild they are familiar with.
Refer to our Skills page for a look at what you're essentially playing to earn more points for.