Nolle prosequi is a Latin term meaning "we shall no longer prosecute". It is a declaration made by a prosecutor in a criminal case or by a plaintiff in a civil lawsuit either before or during trial, meaning the case against the defendant is being dropped. The declaration may be made because the charges cannot be proved, the evidence has demonstrated either innocence or a fatal flaw in the prosecution's claim, or the prosecutor no longer thinks the accused is guilty. It is generally made after indictment, but is not a guarantee that the person won't be reindicted.
In civil cases, a nolle prosequi may be entered as to one of several counts or to one of several defendants. In a criminal case, it has been held improper for a court to enter an order of nolle prosequi on it's own without a motion by the prosecutor. As long a jury trial has not been commenced, the entry of a nolle prosequi is not a adjudication on the merits of the prosecution and the legal protection against double jeopardy will not automatically bar the charges from being brought again in some fashion.
Nolle prosequi is similar to a declination of prosecution, which is an agreement not to prosecute which may be made by an attorney, but also by aggrieved party. In contrast, nolle prosequi is usually made after a decision to prosecute has already been made. A declination of prosecution may be made for many reasons, such a weak evidence or conflict of interest.