Crying lowers the chance of hitting the enemy. Any character that is crying is unable to see where they are aiming, and so, they may miss the enemy. There are rare cases in which the character can connect an attack, but crying makes it hard.
What causes crying has a large list. A few enemies have special attacks that causes the party to cry, such as the Mini Barf's exhaling. Ness and Lucas can also cause crying by using PSI/PK Flash respectively. Enemies can also use Flash to make the party cry. Crying is healed by using Healing α or Cup of Lifenoodles or some other healing item.