This is an elaboration of a (light) stance I took in a philosophy meeting tonight, where we were hashing out the meaning of coolness.
I (lightly) hold that coolness is an impression and awe that people feel towards people with a particular social strategy; this impression is a cousin to respect for leadership, filling some of the same ends.
There are various social strategies for success; being strong, being sneaky, being clever, being a consensus-builder. For prominent members in society (that is, who stand out), they will adopt one or more of these strategies; being cool is a recognition of a certain pairing of being confident and being practical, usually in the context of someone who represents a (strong or weak) alternative or fallback to the existing order. A cool person shares some characteristics of a leader; being prone to making decisions rapidly when needed, not depending frequently on others for support, not being excessively theoretical or principled when doing so would harm his/her posse, and having sparks of potential.