As you raise the Affection levels of the Partners who travel with you, their powers and strength will grow.

When they first join you, their abilities will low, but
as their affection rises, their powers will, too.

When you talk to any partner, you have the option to "Give Present".
When you select this option,
a list of available gift items and
the partners affection level will be displayed.

※Remember, different Partners like different presents.

On the right side of the Partner window
there is a "Heart" or "Diamond" icon,
just click that to show all the available presents to give to them.