perhaps this is a silly question, but i've been battling (fairly casually) for a while now and, while i understand that obviously icons=damage, more icons=more damage=better, i'm still not fully clear on what icons actually mean. do they represent a certain amount of damage, i.e. 1 icon = 20 points of damage (to give a random number)? or is the correlation more complicated than that?

From section 4.2 of this helpful thread:

The guide I linked above goes much further in depth, but basically plug the strength of your pet into the formula above, multiply that number by the number of icons a given weapon does, and you've got your gross damage output (before taking into account a crit, defense, etc.)