A Yellow Card on a character serves as a warning, but will result in a post battle penalty. The possible penalties include the offending unit receiving no experience or AP for the battle, a monetary fine of the player's gil, a fine of items in the player's inventory, a loss of one of the unit's equipped item, a confiscation of the player's law cards, or a permanent unit stat reduction.
A second offense during the same battle or a fatal offense will result in a Red Card and the unit will be sent to jail immediately, just like soccer/football. However, some units (most bosses) have a spell known as Justice that protects them from receiving Red Cards. They will instead receive another Yellow Card upon subsequent or fatal infractions of the law.
A yellow card is shown in many sports after a rules infraction or, by analogy, a serious warning in other areas.