Agility determines who attacks first. Players with the highest agility strikes first. However, as turns go by, a player with a higher agility may be able to make two or more attacks before another player (SNS version only). However, agility is not the same as speed.
In the iOS version, players with the highest speed gets to move first in an order. Unlike the web version, characters and enemies in the iOS version won't have multiple turns at once.
Players initially start off with an Agility of 5 on both versions. Agility increases by increasing the Wind Attribute, which increases Agility by 1, or by leveling up, which increases Agility by 1. Also, the Eight Extremities talent skill, Eight Extremities Strengthen, permanently increases the user's Agility by a percentage amount.