Split farming
Split farming is the practice of multiple players in a game splitting up 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 play on a low difficulty level (usually Normal), and each head off to a different bounty in the Act, in order to complete the entire act and earn the Horadric Cache reward from Tyrael as quickly as possible.
Split farming is most commonly found in Act One, since the Ring of Royal Grandeur can only be found from Act One caches. If/when cache distribution changes, or that ring begins to drop from other sources, or other highly-desired cache-only items are added, player split farming behavior will surely change.
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.
Developers Disapprove
The Developers have several times said they don't like the play style that split farming incentivizes, and while they've made some tweaks to make it 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.[1]