The Chosen are individuals so named because at least part of their great martial and magical power derives from having been picked to be one of the direct agents of one or more deities; each of the Chosen are a force to be reckoned with.
They are not gods, though they may appear as demigods, and truly, the distinction will certainly seem to be near meaningless to any hapless mortal that has to stand against them.
Most famous of the Chosen is surely the Three-Eyed King, Archaon the Everchosen, supreme commander of the forces of Chaos. Empowered by all the Chaos Gods -- save the Great Horned Rat, whom he despises -- it was Archaon that brought the Mortal Realms to the very edge of defeat during the Age of Chaos.
Nagash's forces are led by his dread Chosen, the Mortarchs, immensely powerful Deathlords directly empowered by their Undying King. Each serves Nagash in their own way, performing whatever is requested of them, while otherwise ruling over portions of his vast empire in Shyish.
While each Mortarch is phenomenally dangerous, it is, perhaps, the spies of the ancient Vampire lord Neferata, and Orpheon Katakros' legions of Ossiarch Bonereapers, that give Nagash's enemies the greatest concerns.
Within Azyr, the Celstial Realm, the Chosen known as the Six Smiths forge the weapons of the Stormcast Eternals as well as their very souls, as they oversee the foundries of the Sigmarabulum and every Reforging on the Anvil of Apotheosis. The Six Smiths are all heroic scions of Grungni, but much about them has been obscured.
Some would argue that the Soulbound themselves are Chosen in the service of Order. However, were a lone Soulbound to stand against one of the true Chosen the terrifying disparity would swiftly become apparent.
- Warhammer Age of Sigmar Roleplay - Soulbound (RPG), pg. 258