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Wiktionary
service of process

n. 1 (context legal English) The delivery of information to a person or entity providing notice that they are being sued with sufficient detail for them to respond to the suit. 2 (context legal English) The effective notification of a lawsuit such that a court may proceed with the case.

WordNet
service of process

n. the act of delivering a writ or summons upon someone; "he accepted service of the subpoena" [syn: service, serving]

Wikipedia
Service of process

Service of process is the procedure by which a party to a lawsuit gives an appropriate notice of initial legal action to another party (such as a defendant), court, or administrative body in an effort to exercise jurisdiction over that person so as to enable that person to respond to the proceeding before the court, body, or other tribunal.

Notice is furnished by delivering a set of court documents (called " process") to the person to be served.