The main purpose of this type of farming is to amass faction with the Kurzicks to progress towards the allegiance rank or increase Allegiance skill effectiveness for PvE use. Faction farming is commonly practiced by members of an alliance trying to increase their alliance faction with either nation to gain control of towns.

WHAT IT TAKES TO OWN A TOWN
House Zu Heltzer: 54,903,365
Altrum Ruins: 28,903,365
Tanglewood Copse: 15,651,419
Saint Anjekas Shrine: 9,871,733
Lutgardis Conservatory: 9,268,813
Braur Academy: 7,416,965
Vasburg Armory: 6,980,456
Durheim Archives: 5,057,524

There are a few areas that players go to Farm Kurzick Faction. These are:
Compete in Alliance Battles, accessed via your Guild Hall.
Competitive Missions: Fort Aspenwood and the Jade Quarry.
Challenge Missions: Altrumm Ruins and Amatz Basin for the Kurzicks.
Killing Level 20+ foes in Echovald Forest with Blessing of the Kurzicks
Doing repeatable factions quests.

Fast Faction Farming [FFF]
FFF is an abbreviation for fast faction farming, the faction in question is usually Kurzick Faction but the concept can apply to Balthazar Faction. The emphasis in fast faction farming is on getting as much faction as possible in as little time as possible to allow for many runs to be done quickly.
There are multiple ways of fast farming, but the fastest two Kurzick methods known at this time are:
1. The FFF run outside of Lutgardis Conservatory. This run is based on the repetitive completion of the quest Securing Echovald Forest. On average, the run produces 400 faction, 2000 XP and 150 Gold every minute for proficient teams.
2. The FFF run outside of Altrumm Ruins. This relies on farming the wardens and four closest bosses in Arborstone in Hard Mode. On average, it produces 1400 faction in 3 minutes for proficient teams.