Most crimes involve intentional conduct. For example, in some states, the offense of assault can be comitted by the defendant intentionally using or attempting to use force against someone, as with a punch or kick. By way of comparison, the unintentional use of force against someone—for instance, raising one's arms in celebration and accidentally hitting someone—doesn't constitute an assault.
But some crimes involve reckless or negligent, rather than intentional, conduct. The term "reckless" essentially describes a defendant's simultaneous understanding and disregard of a substantial risk of harm. An example is a defendant having previous DUI convictions and understanding that driving drunk can harm or kill people, but nevertheless getting behind the wheel while intoxicated and causing a fatal accident. (See What amounts to recklessness?)
Negligence is a concept invoked more frequently in civil, rather than criminal cases. (See Negligence, The 'Duty of Care,' and Fault for an Accident.) That's because conduct that involves ordinary negligence, like becoming distracted while driving and rear-ending someone, typically isn't enough for a criminal conviction.
But negligence also has a place—right next to recklessness—in criminal law. Some courts draw a distinction between the two terms, explaining that recklessness requires that the defendant actually appreciate the risk in question, while criminal negligence occurs when the defendant should have been aware of the risk. (See Ex parte Koppersmith, 701 So. 2d 821 (Ala. 1997).) But in practice, the concepts are difficult to distinguish, and many courts and legislatures use "criminal negligence" and "recklessness" interchangeably.