Before presenting their oral arguments, lawyers for both sides submit briefs, which summarize the facts of the case, provide supporting evidence, and
detail the legal reasoning behind their arguments.
Image source: Wikimedia Commons, United States Department of Justice. Public Domain.
Briefs are often also filed by "friends of the court" (amicus curiae).
"Friends of the court" describes a person--or organization--who is not part of the lawsuit, but has a strong interest in the case.