Dead or Alive
There are two major states-of-being in Demon's Souls: alive or dead (a phantom). You can progress through the game in either state, and each has different multiplayer options available to it. The advantage to progressing while alive is health because health is capped at a percentage when dead. It may seem obvious that being alive is advantageous, but you can progress as a phantom, and how you resurrect is up to you.
There are three ways to resurrect. The first is to defeat a boss while dead in your own game world. The only way to do this is alone, with a fraction of your life.
The second and third involve entering the world of a living player. You can enter as a "blue" or "black" phantom. To enter as a blue phantom, you place a marker in the world. If a living player sees it and summons you (only living players can), you will join his world. If you or he dies, you return to your world with full health and only lose time. If you live long enough to help him defeat a boss, however, he will move on to the next challenge, and you respawn at the beginning of your level, alive, and with the knowledge of how to successfully defeat the boss (and potentially get past other challenges along the way), as well as summon blue phantoms of your own.
If you choose to enter another world as a "black" phantom, it picks a random living player and you invade his world. He gets a message that warns him of the event. If you hunt down the player (with a limited life bar, mind you) and kill him, he respawns dead, and you respawn alive. If he kills you, you stay dead (I don't know if there are other disadvantages). Living players cannot prevent an invasion, but they will see a message notifying them of the invasion, and may have tools for banishing you or making it difficult to defeat them.
Everything you kill gives you souls. Souls are your only currency, used to do everything from buy equipment to level up. When you die, all of your souls are dropped where you fell, but the level (yes, including enemies) is reset. And since only one pile of souls can exist at a time, if you die while returning to recollect your pile of souls, a new pile is dropped, and the former disappears forever. This also happens a lot, and is really painful.
Those are the two unusual systems I want to describe as reference to the experience they create, so I can in turn describe why they seem important.