What is Hardcore Survival Multiplayer (HCSMP)? Well, its a somewhat newish style of playing minecraft online. IMO by far the most intense. 
If youv ever played hardcore mode on single player, just imagine that but online and with PVP.

Basically you start out on the server with one life. Once your killed, the server automatically kicks you from the game and bans you. Don't worry though, its not permanent! Many servers will allow you to rejoin after a week or two. Some go as far as one month + bans, others as little as 1 day or even just a couple of hours. 

The main goal is to survive as long as you can. PvP is typically enabled as well, so you must always watch your back and be careful who you decide to work with, as they can turn on you anytime. Fight off players, raid bases, set up traps and defenses, farm and keep a constant supply of food... and more! Hardcore servers definitely keep you on your toes

This genre only started a few months ago, so their are only maybe 20-30 servers in total right now. If you guys are interested in testing your might, check out alist of servers on http://tophcsmp.com