Farming is a term commonly used to refer to killing Monsters for items that they drop, particularly valuable ones as a way of making gil. A few such items are sold to NPCs or used in Quests, but most are sold to other players via the Auction House. Farming usually involves killing monsters that are Too Weak, since they can be killed more quickly and with less risk, but Easy Prey are sometimes targeted because they can drop crystals, Beastmen's Seals, and at higher levels Kindred's Seals in addition to their normal drops. Players farming Easy Prey generally receive Signet, Sanction, or Sigil so that crystals can drop. Both Sigil and Sanction can provide additional bonuses that help reduce downtime.
Many players use Thief as their main or sub job while farming for its Treasure Hunter ability; Ninja is also popular for its ability to avoid damage with Utsusemi, and White Mage or Dancer for jobs that can't normally heal themselves, to reduce downtime. Adventuring Fellows are sometimes used to speed up killing or reduce downtime, especially at higher levels. If the monsters being farmed are hard to find, Wide Scan may be useful. Red Mages can be used too for farming at higher levels. They have additional effects for their weapons and guarding spells to defend themselves. Refresh in combination with Convert gives them almost no downtime at all. So the ability to pack a punch, to heal themselves for MP and HP, and to defend themselves makes them ideal main jobs for farming.
Gil Guide by InfamousDS (Not technically farming, but lists some Gil drops)