Hardcore mode is the mode where you go in a survival world like normal but the difficulty is really hard, The spawn rate of mobs increases, and every danger increases with it. If you get stuck in a cave there is a high chance that you will get hunted down by the zombies or blown up by a creeper who just spawned right behind you just now or you could get shot by a skeleton.
Also, You only get one life in this mode which means if you die you die.