East Coast people say affidavit of service, but Californians usually say proof of service. If you don't say either because you don't know what they are, you've come to the right place. Both terms refer to a legal document that evidences the fact that certain other documents were "served on" a party to a lawsuit. "Served on" is another legal term of art, and it has nothing to do with service with a smile.
Imagine a world in which you could sue somebody in court but not tell them about it until after you had received a big judgment against them. It's straight out of Kafka and not likely to happen in the near future in the United States. In fact, you can't even initiate a lawsuit today without telling the other party about the case. Mentioning it to them in passing isn't enough. The courts want to be certain that the other person knows about the case, so they require a process called "service."
"Serving" a legal document means that you get the document to the other party in one of the ways the court authorizes. That means you can't just go by and heft it at their door as if you were a newspaper delivery kid. Instead, you must use a manner of transferring it that ensures that it comes into their hands. Perhaps the most used method of personal service is to have another adult, not a party to the lawsuit, take the documents and personally hand them to the person you are suing. You can ask a friend to do it, or you can hire a company of process servers.
Regardless of whether you hire a process server or ask your college roommate to serve legal papers, the court needs to hear from that person. Whoever serves the papers has to fill out a paper under penalty of perjury telling the court what documents were served, when, where, to whom and how. This is called an affidavit of service or proof of service. Many courts provide forms that the person can use to create this document, and process server companies have their own process server forms.
The purpose of an affidavit of service is to provide sworn testimony to the court that the legal papers in question were properly and legally served on an individual. If affidavits of service did not exist, the person who served the document would have to appear in court, raise a hand, swear to tell the truth and nothing but the truth, then describe serving the document. This would take a lot of the court's time, as well as a lot of the process server's time.
Not every document has to be personally served on the other party. This is necessary for only some types of legal documents like those opening a lawsuit, or things like eviction notices. Once a party has appeared in court, other parties can serve him or his attorney by mail. That saves time and money and, since the party already knows about the lawsuit, it is more likely that he will expect and look for the legal documents that are part and parcel of a court case, like motions, briefs, status reports and so forth.
The copy of one of these documents filed with the court must have an accompanying proof of service. The person mailing the document is required to fill out a proof of service by mail form, swearing under penalty of perjury that she mailed a particular document to a particular person on a specified date and time.