Have you noticed those symbols under the monsters name when you select to attack them? They indicate the monsters strength and weakness.
The three symbols are:
If you are unsure of what type of attack a weapon does, you can check in the equipment screen.
When you travel from one place to another, the days pass, and eventually the season changed (Sprout -> Bud -> Flower). So what do seasons affect?
Recruiting characters (characters may appear in some seasons and not others)
A lot of people are having trouble working out what the statistic symbols mean, since it's not explained in the instruction manual. Here's an explanation:
Sword: Physical attack power
Shield: Physical defense power.
Magic Wand: Magical attack power.
Shield: Magical defense power.
Hand: Skill (hit% and multiple attack potential)
Running Man: Speed/Agility (speed that the character acts in battle)
Star: Luck (critical hit rate)