Latent Effects are effects that only are triggered if a set condition (or conditions) are met in Final Fantasy XI. These are generally listed in the profile of the specific item, or else they are referred to as Hidden Effects. That said, the latent effects are somewhat enigmatic since the triggers are not immediately apparent.
Latent Effects can be as simple as having an appropriate Support Job equipped or may have multiple triggers, for instance a Minstrel's earring will give 30% reduction from physical damage only if the Bard wearing it has less than 100% TP and less than 50% HP. They are useful both in terms of the bonuses they give, but they serve as an indicator on some equipment, such as the elemental resistance offered by a weapon of trials.