Amicus curiae
The situation most often noted in the press is when an advocacy group files a brief in a case before an appellate court to which it is not a litigant.  Appellate cases are normally limited to the factual record and arguments coming from the lower court case under appeal. Usually attorneys focus on the facts and arguments most favorable to their clients.  Where a case may have broader implications, amicus curiae briefs are a way to introduce those concerns, so that the possibly broad legal effects of court decisions will not depend solely on the parties directly involved in the case.