A memorandum, in general, is a brief writing, note, summary or outline. It is an informal record or outline of something which may or may not be detailed later.
A "memorandum of law" may be prepared by an attorney to support a legal argument, which is similar to a brief but with less attention to legal writing formalities. It contains legal arguments based upon the lawyer's understanding of the law applicable to the issues and is often supported by citations to legal authority. A "memorandum of decision," or "memorandum opinion," is a short statement by a judge announcing his/her ruling without explanation or giving detailed reasons, which may or may not be followed by a more thorough written decision.