A party is one of the people or entities involved in the legal matter. Legal matters are usually referred to by using the names of the parties i.e. Smith v Jones.
A party who brings a claim is known as a plaintiff (or occasionally, the applicant), and a party against whom a claim is brought is known as a defendant (or respondent). In an appeal, the person who lodges the appeal is called the appellant and the other side is called the respondent.