Deathspammers are players who flood the chat with death messages by repeatedly committing suicide. While normal chat spammers can simply be ignored individually using the /ignore command, the same is not true for death messages which can only be disabled entirely.
Players usually use two methods for death spamming. The first is simply setting your spawn point near a lethal drop and enabling autowalk and autorespawn, resulting in repeated death by fall damage. The second and more widely used method is to set a spawn point in the path of hostile mobs which can kill the player very fast. If they are renamed then they will not despawn and they can be used to convey messages in chat (ie. Player was killed by [message]). This was used during the Kinorana Map Crisis to spread anti-Kinorana propaganda.