The act of showing up in court as either plaintiff, defendant, accused or any other party to a civil or criminal suit, either in person or, more frequently, by filing a document to that effect.
It implies that you accept the power of the court to try the matter (i.e. "jurisdiction").
Appearances are most often made by lawyers on their client's behalf and an appearance by a lawyer binds the client.
You can make a limited appearance called a "special appearance" in which your presence is not to imply acceptance of the court's jurisdiction but, rather, to challenge the jurisdiction of the court.
An example of the usefulness of a "special appearance" would be where you want to raise the fact that you were never properly served with the court papers.