Recklessness

The Model Penal Code defines recklessness as

A person acts recklessly with respect to a material element of an offense when he consciously disregards a substantial and unjustifiable risk that the material element exists or will result from his conduct.

I pulled the definition from the criminal code because that's where recklessness is most often used as a legal tool. The key phrase here is "disregards a substantial and unjustifiable risk." The risk must be substantial (not imaginary) and unjustifiable (there must be no good reason for disregarding the risk). The justification is proportional to the gravity of the risk (you'll have to work hard to find a justification for homicide, for example).

If that doesn't make any sense, just understand that if negligence (to be defined later) is stupidity, then recklessness is either extreme stupidity or borderline purposeful stupidity.