When prosecutors file a “discontinuance”, they are basically notifying the court that they will not further prosecute the case. They do this by filling out a discontinuance document then submitting it to the court that is about to hear the case.
A discontinuance is different from a “not guilty” verdict. Although the accused doesn’t get prosecuted, it doesn’t mean that the case cannot ever be restarted. There are, however, only very rare instances when cases for which a discontinuance has been entered were again brought up against an accused.