Answer:
Criminal offences are offences you can be prosecuted under the law for. Noncriminal offenses are things like libel or slander, and causing unintentional injury (a big passion of many compensation-seeking people) and depending on which country you live in, these can only be pursued under a civil prosecution. Civil prosecutions are not funded by the government - and are instead funded by an individual or organisation. For example - if I said my friend is a horrible person, and posted it on the Internet or published it, then they would be entitled to seek civil prosecution if they had the money and time. These are often to prove a point to others (e.g. that my friend is not horrible) and can often cost more than they gain. Unfortunately, this is an aspect that some newspapers exploit to print false statements about celebrities.