We have 10.0g solid KMnO4 dissolved in 500.0 mL of water. The temperature changes from 24.8 C to 23.5 C.
I found the heat of the reaction. It is 2770 J. But I cannot figure out what the molar heat of solution for KMnO4 is. I am not even sure what molar heat of solution is. Is it the heat energy in one mole of the substance? Would it then be 2770J/#of moles of KMnO4?

The heat of solution is the heat evolved (or absorbed) when something is dissolved in water. In your case, you want the heat per mole of the material. You have 10 g of KMnO4 so you should be able to figure out how many moles you have. You know the volume of water. The temperature cooled from 24.8 C to 23.5 C, a change of 1.3 Celsius. The specific heat of water is 1 cal/(gram-deg C). You can look up or calculate the specific heat in joules per gram degree C. From the mass of water and the temperature change, you should be able to figure out how much heat evolved (apparently you already did that). So, all you have to do is divide that by the number of moles of the material.