The Basilisk in the lower areas of Depths and The Great Hollow as well as Seath the Scaleless in The Duke's Archives and Crystal Cave can curse the player. When you are first cursed, you die and a statue of your body appears in the game. If you play online, you will be able to see the statues of others as well.
If you are cursed while playing online as a summoned or invaded played, you simply die and respawn as per normal.
When you respawn at a Bonfire, you have 50% of your health. You can not Revive or Kindle at Bonfires. It is possible to collect Humanity, and you can still use an Estus Flask to recover up to 50% of you health.
You will stay cursed until you are cured.
If you are Cursed, a statue like this will appear. If you are playing online, others will see this statue.
Wearing the Cursebite Ring helps a lot. Most armour has a Curse rating, the higher the better. The Crimson Set or the Antiquated Set can both be picked up early in the game and have a good resistance level.