A Bench Memorandum(also known as a bench memo) is a short and neutral memo

Memorandum

A memorandum is from the Latin verbal phrase memorandum est, the gerundive form of the verb memoro, "to mention, call to mind, recount, relate", which means "It must be remembered ..."...

 which summarizes the facts, issues, and arguments of a court case. Bench memos are used by the judge as a reference when preparing for the trial, when hearing the lawyers' arguments, when drafting a decision, and just generally to give the judge an idea of what the arguments given by each side in the court case will be. Bench memos are generally written by the judge's law clerk

Law clerk

A law clerk or a judicial clerk is a person who provides assistance to a judge in researching issues before the court and in writing opinions. Law clerks are not court clerks or courtroom deputies, who are administrative staff for the court. Most law clerks are recent law school graduates who...

, although lawyers can also submit their own memos that argue their case, making sure that the memo remains neutral.