From Diablo Wiki
Nephalem Trials were planned as a feature in Reaper of Souls, but did not make it into the game. They were going to be arena-like mini-dungeons accessed through "Death Orbs" that players could encounter in any dungeon in the game. In a Nephalem Trial player(s) would have faced huge waves of incoming enemies, and earned rewards for surviving through higher and higher numbers.
- In retrospect, this feature seems to have morphed into the small horde or five-wave events tied to Cursed Chests and Cursed Shrines. Also, Patch 2.1 added the "fight endless waves of enemies" Realm of Trials mini-dungeon as part of the Greater Rifts feature.
Nephalem Trial Details
This feature was first revealed in Blizzard's official Reaper of Souls FAQ, in a section about new game modes:
Postponed from RoS Release
In November 2013 Blizzard announced that Nephalem Trials were not going to be ready when Reaper of Souls was released, though they hoped to patch them into the game (and into D3V) sometime afterwards. 
Rather than delay the release of the expansion to make sure Nephalem Trials could make it in with all the necessary components, we made the decision to cut them for now and re-focus our efforts on making sure other key systems like Adventure Mode, Bounties, Nephalem Rifts, and Clans & Communities (just to name a few) are solid. It’s not an ideal scenario, but these are the kinds of hard calls we sometimes have to make in a world where we can't stack +Maximum Resource.
The gameplay felt great and was in a good place at gamescom 2013 where we announced them – which is actually why a lot of the individual Trials have been added on their own as standalone events into Reaper of Souls – but the mechanism that made the overall system feel meaningful over a long period of time wasn’t and would take some pretty significant tech and time to implement (in this case, at the expense of other features as well).
Code strings in early Reaper of Souls datamined information list a number of types of Nephalem Trials. These are early versions of the content and may be entirely different in the final product.
- Berseker Trial – Slay monsters before they become enraged! Killing marked monsters before they enrage grants bonus experience and gold!
- Collapsing Dungeon – Loot Nephalem Relics to delay the dungeon collapse and earn time bonuses!
- Goblin Hunt – Find the treasure goblins before they all escape!
- Horde Trial – Slay an unending horde of monsters. Kill monsters before the timer ends to earn bonus experience and gold for every kill!
- Nephalem Trial – (No details provided.)
- Wave Trial – Destroy each enemy wave as quickly as possible. Extra time is converted into bonus experience and gold!
- Nephalem Trails released prior to RoS CM, Blizzard Entertainment, 22/08/13
- Nephalem Trial details - Blizzard Entertainment, 23/08/13
- Reaper of Souls FAQ Blizzard Entertainment, 21/08/13
- Blue Post Diablo.IncGamers.com News, 13 November, 2013
- Reaper of Souls Datamined IncGamers, 12/09/13