Agility (AGI) is associated with the element Wind in FFXI and when compared with an attacker's Dexterity it serves to determine the likelihood of being critically hit. Higher Agility will, of course, reduce chances an attacker will land a critical blow.
Evasion and Ranged Accuracy are also said to be boosted by a character's Agility where 2 AGI equal 1 point in Evasion or Ranged Accuracy.
For the Thief job, Agility also plays an additional role. When used with Trick Attack, Agility becomes a damage modifier as well adding an extra 1 base weapon damage per AGI on the next hit after Trick Attack is engaged.
Because Agility is such an important stat for the Ranger job, this compares the Agility of a level 1 Ranger of all five races in Vana'diel.
Some players, upon reaching level 75, will decide to permanently boost their Agility through Merit Points. For others, however, this isn't a viable option whether it be because of level restrictions or simply because they're leveling up an alternate job for a change of pace. For these people, choosing gear and food to boost their Agility stat is the answer.
A comprehensive list of Agility-boosting foods can be found on the Agility Food Page.