| radiant is a keyword that describes the type of damage the attack does. Many undead are vulnerable: radiant which means they will take extra damage on a radiant attack. On the other hand many angels are resistant radiant, meaning radiant attacks do less damage. Similar to elemental idea of fire doing more damage to ice creatures.
Simple, military, and superior are weapon levels if you will. Simple is the weakest, military is the middle, superior are the "best". Melee and ranged are also classifications of weapons. So for example,
Paladins are proficient (they gain the proficiency bonus) with
Simple melee, military melee, and simple ranged. This means they get the proficiency bonus described in the weapons section of the phb while using weapons under these classifications. | 
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