From Diablo Wiki
Split farming is the practice of multiple players in a game spreading out to farm items or other valuables more quickly than could be done alone, or in a collected group. The most common form of split farming is found in Adventure Mode, where players all head off to do different bounties in the same act, thus completing them more quickly than is possible solo, and all partaking in the Horadric Cache reward.
While the developers have said that they don't approve of split farming and feel it's not how the game is meant to be played, they have made few changes to make split farming less viable or valuable, and added many features and game mechanics that make split farming the smartest way to play, at least when seeking Horadric Caches or Infernal Machines.
Split Farming in Adventure Mode
There was little incentive for split farming in Diablo 3 prior to Reaper of Souls and the introduction of Adventure Mode. In Diablo 3 vanilla players would sometimes spread out to find something more quickly, such as the exit from a level or a keywarden, but those were usually players on the same level, spreading out to search more quickly.
The real value of split farming came from completing bounties in Adventure Mode. In the initial Reaper of Souls system, every character in the game received the experience and gold bonuses for each bounty, regardless of their location when the bounty was completed. (This was even more valuable during the Reaper of Souls beta test, when every bounty rewarded a small cache bag, with a bigger bag for completing all five bounties in an act.)
Split Farming was made somewhat less valuable in a patch shortly after Reaper of Souls' release, when bounties were changed to only award their experience/gold value to characters who were near the monster/event, or on the level the bounty was awarded for. The awarding of a Horadric Cache to every character in the game, no matter their location, was not changed in this patch, and thus split farming continued on as a popular tactic for players seeking Cache-only items, chiefly the Ring of Royal Grandeur.
Infernal Machine Farming
Keywardens have always been a useful enemy to split farm. True split farming wasn't useful on Keywardens until Patch 2.1, when the keys they dropped were made Global drops.
Prior to that patch, going all the way back to Diablo 3 vanilla, players would spread out to find the Keywarden more quickly, but everyone would do so in the same area at the same time. The point was to search more quickly, and when someone found the KW they would announce it, and then wait until the other players could run over before killing the KW. This was necessary since prior to global drops, the KW dropped like any other monster, and thus only dropped items (including the Key) for characters who were nearby when it died.
This changed in Patch 2.1, at the start of Season One, when KeyWardens were made Global Drops. This meant that the KW would drop items for every character in the game, no matter where they were located when the KW died. Thus players could all head off to hunt them, up to 4 players each in a different act, and only when someone found and killed the KW would they announce if it had dropped a key, since if it dropped a key for one player, it would drop a key for everyone. (And if not for one, then not for all.) Players then had to wait near the KW until the other players in the game could portal over, otherwise it was hard to find the corpse and the key not knowing where to look on the entire map.
Horadric Cache materials
Patch 2.3 introduced Horadric Cache materials, which greatly incentivized split farming bounties in all five acts. Rather than just Act One and occasionally some other Act, in Patch 2.3 players need to collect Caches from all five acts to obtain the legendary materials inside them. When earned, Caches are awarded to everyone in the game, regardless of their location or participation in any of the bounties in that act.
The Developers have several times said they don't like the play style that split farming incentivizes, and while early in Reaper of Souls they made some minor tweaks to make split farming less rewarding (requiring players to be near the Bounty target to earn the reward), that's done nothing to lessen the practice, since the main goal remains the Horadric Cache for completing the entire act of bounties.
Travis Day spoke on split farming during the Reaper of Souls beta, in January 2014.
Game changes dating to after Travis' comments, such as making KeyWarden drops global and adding Horadric Cache materials in Patch 2.3 have done nothing but encourage Split Farming, so clearly it's not high on the developers list of player behaviors to fix or change.