Resplendent Chests is the term for the shiny, glowing, big-dropping special chests found in Diablo III. These chests are generally found in fixed locations on surface areas, and while their locations can vary in the randomly-generated dungeons, they are seldom fully random, but will generally be found in known locations; just past big bosses, in certain locations at the end of a level, etc.
Resplendent Chests are visually distinct from normal chests, and drop considerably more items. It's not yet known how the math works on such objects -- do they drop higher quality items, or just more items?
In Patch 1.0.5 Resplendent Chests were improved further in [[Inferno] difficulty. Since that patch opening a chest will grant one stack of Nephalem Valor and loot will be affected by how many stacks of Nephalem Valor the player has when they open the chest
A Wizard exults in the big graphical display that accompanies a transcendent chest.