An esper will grant 1% of its stats to the unit to which it is equipped. For example, if Ifrit has 3,400 HP, it would add 34 HP to any unit it's equipped to. This includes MP, attack, defense, magic and spirit.

The spirit stat affects your unit’s magic defense as well as the recovery strength of white magic curatives like Cure. Also, any unit equipped with an Esper can use the skills the Esper has learned.