To argue is to present an argument. In criminal law, argument refers to the persuasive statements either the prosecution or defense make to the judge or jury on behalf of a client. For example, an attorney goes to court to argue a motion or to argue an appeal of a court order. A Memorandum of Points and Authorities in a brief, which sets forth the party's analysis of the law in relation to the facts and explains why the judge should find in that party's favor is referred to as a “Legal Argument.”
An “Oral Argument” is a lawyer's spoken presentation to the court detailing the legal and factual reasons why the judge should make a decision favoring the lawyer's client. “Oral Argument” also refers to a type of hearing where the judge hears arguments from both opponents. Finally, at the end of a trial, the prosecution and defense will give a “Closing Argument,” where they are allowed to summarize their case in front of the jury.