World bosses spawn in one of several set locations in Madrigal in Channel 4 (Activities). The location of the boss is given as a server-announcement when it is spawned. If you're in Channel 4 and on the same map as the World Boss, you can see its specific location on your map.
In order to claim rewards for world bosses, you must exceed a certain damage threshold on the boss (which is typically very easy to fulfill), and its HP will scale with the number of players who have hit it.
The most common World Boss is the Dragon of Madrigal, oftentimes shortened to DoM.
The primary drops from DoM are angelic bead shards, used for powerful pet beads. DoM can also drop itself as a pet, but this is very rare.
You must be at least Level 121-H to obtain rewards from fighting DoM.
Adrozas is a level 150 World Boss found in Eldeon. If you defeat Adrozas, there's a chance he'll drop a Piece of Cloth, a rare item required to craft the legendary Yggdrasil Sets. Other drops include Angelic Bead Shards and Supreme Clockworks Boxes.
Basilisk of the Great Maw
The Basilisk of the Great Maw is a World Boss that spawns in Bahara Desert in the Basilisk Nest. If you defeat it, there's a chance you'll be rewarded with special set jewelry from the Savage Wilds dungeon.
[General] Razgul
Razgul is a World Boss that spawns in Valley of the Risen, which has a chance to drop the Gimore of the Risen book, used by Mentalists.
Chief Keokuk
Chief Keokuk is a World Boss that spawns east of Kaillun Grasslands, and has a chance to drop Savage Wilds jewelry pieces when killed.
Guan Yu Heavyblade
Guan Yu Heavyblade is a World Boss that spawns in Traseia (Layer 1), which has a chance to drop Guan Yu's Shell, a shield skin.
Iblis' Perpetrator
Iblis' Perpetrator is a World Boss that spawns in Dark Traseia (Layer 1).