Negligent homicide is the unlawful killing of another person due to negligent behavior without any intent to harm or kill the person who died. It is also sometimes referred to as "involuntary manslaughter".
If you kill another person, this is the least serious of the criminal charges you might face in the U.S. and in countries with similar laws (the other possible charges being degrees of murder and manslaughter). The precise definition and punishments for this crime vary by state/nation and circumstances, of course. Individual U.S. states make their own laws about what constitutes homicide, although state laws are generally similar until you get down to fine details. The federal goverment does not involve itself with homicides unless they are crimes that can result in a death sentence or which were committed on federal lands.
People who might be convicted of a more serious charge (say, second degree manslaughter) may be offered a plea bargain in which they plead guilty to the lesser charge in situations where the district attorney is eager to have the case finished up.
Some U.S. states make a distinction between negligent homicide and criminal negligent homicide based on whether the killer displayed simple negligence or criminal negligence. Criminal negligence is generally considered to be really extreme negligence, i.e. negligence above and beyond what might have been caused by simple everyday inattention, or dereliction of duty.
For instance, a babysitter who leaves a toddler unattended near a wading pool for a few minutes to answer a phone -- and consequently the child drowns in the shallow water -- is negligent.
A parent who leaves a toddler locked in a car in a mall parking lot on a hot summer day for several hours to go shopping, resulting in the child dying of heat stroke, is criminally negligent.
The wading pool incident wouldn't likely result in criminal charges unless the babysitter had a history of child neglect, whereas the death of the child in a locked car would almost certainly result in a negligent homicide or manslaughter charge because the parent had done something that any reasonable person should know not to do.
For another example, take two nurses whose actions result in a patient dying.
Nurse A misreads a patient's chart and administers an antibiotic the patient is allergic to; the patient goes into shock and dies. The nurse is negligent and she and/or the hospital is likely to be sued, though she might not be charged with a homicide.
Nurse B hears that an elderly patient has buzzed for assistance, but she's busy making out with an EMT in the broom closet. The patient buzzes again, and the nurse continues to ignore it. When she finally checks on the patient, she discovers the old man dying of a heart attack. Had she responded as she was supposed to, the patient would have been saved; thus, this nurse has committed criminal negligence.
Criminal negligence -- and thus criminal negligent homicide -- is a much more serious crime than regular negligence.
Criminal negligent homicide is treated as a felony that will result in a large fine and/or prison term, possibly one of more than a decade. In some states, simple negligent homicide (particularly in cases of vehicular homicide) may be treated as a misdemeanor that results in a fine or brief (a year or less) jail term.