To begin with: Batman doesn't have special powers. He is the epitome of the answer to "what would you do with your life if money were no object?" The answer: I'd dress up as a bat and fight crime to avenge my parents' murder! He's filthy rich and physically fit as all hell, but Batman has no special powers.
Special powers are powers that make a given person (or character) stronger, faster, or better than your average Joe in some respect. This can be associated with an emotional trigger, a talisman of some sort, or be inherent. Some examples:
Characters like Batman, the Punisher, Rorschach, and many others are popular because they have no special powers; they simply possess the willpower, resources, and foresight to accomplish any goal they set their mind to, and to accomplish any challenge that presents itself.