Excellent question! When you hover over one of your units before selection and entering into the fight, it is showing you that your unit, in this specific case, is stronger or equivalent to the red fist enemy unit, which is the icon used for all heavy melee troops. When nothing shows up over the enemy, it means that that unit is weaker than the enemy unit. Each type of unit has an icon to denote whether it is heavy melee (red fist), light melee (blue sword), light ranged (green arrows), magic (purple... thingie), and heavy ranged (yellow fireball), and all units fit into one of theses categories. Different types are stronger and weaker in comparison to other types, and choosing units to send into a battle that are stronger against the enemy results in fewer losses. Light ranged and mages receive certain boosts when fighting against heavy melee, for example, such as doing more damage or lowering the defense of the enemy unit they hit with an attack.
For more in-depth information on what each unit is best for, you can click on the little "I" in the upper-right corner of the unit portrait to open up its description.
...And this is probably a fairly confusing explanation, but I do hope it makes sense.