Love Augment works like Attack with additional attack bonus based on how many battle Cecil have covered party members. 

I highly recommend maxing Love Augment (cap at 99) if you want your second and third playthroughs faster especially when you use Safe Travel since you can't level up your characters, it'll help clear early bosses in a few hits. It also help you with tail hunting.

Maxing Love augment is about 45 min, here is the fastest strategy:

• Buy 99 Sirens.
• Equip Cecil with Kick (first slot), Cover augments.
• Kill all you all party members except Cecil.
• Use Phoenix Down to revive Rosa (or any one you like), her HP will be in critical (yellow) and this will activate Cover Augment's passive automatically during battle.
• Go to Mist Cave and use Siren inside; you will always encounter 4 Goblins.
• Wait Until Rosa is hit (Cecil will cover Rosa automatically), then use Kick to kill all of them.
• Repeat this 99 times.

To check how many cover you have provided, simply go to menu -> ability -> select Love Augment.