What exactly do Defense and Resolve do, mathematically?
Defense is a flat reduction to the HP damage taken by the target, applied after resistances; Shield Defense and Lust Defense are the same, except for Shield damage and Lust damage, respectively. For example, if you take a 30 damage Electric attack with 50% Electric resistance and 5 Defense, the 50% Electric resistance reduces the damage to 15, then Defense is subtracted from that to give a total damage taken of 10.
Resolve increases Willpower by its value and Max Willpower by half its value. For example, if you have 6 Resolve, you'll gain 3 Max Willpower and 6 Willpower. As such, it indirectly increases Lust Defense (since it's equal to Willpower/5 for Steele and Willpower/4 + Level for everyone else) and increases the chance you'll pass Willpower checks, which generally leads to resisting enemy psionic attacks (and some lust-based ones) or getting better outcomes in certain non-combat scenes.