On Minecraft Hardcore servers you're playing in Hardcore mode, but unlike in single players where the game would end, on Hardcore servers you would get banned or temporary banned from the server after dying.
Bans and temporary bans on Hardcore Minecraft servers
Depending on gamemode and server, you get banned or deathbanned. Some servers would ban players until server has had full reset while others would deathban player for anywhere between 1 hour and a few days.
Stakes are higher on Hardcore servers
Because of bans and deathbans stakes are higher on Hardcore Minecraft servers, which is why most of players are super cautious and always geared up, ready for fight.
Hardcore servers usually allow both stealing and griefing and generally don't have many rules, but be sure to check them out before doing something that could get you banned.
