Agreement by the defendant (or the defendant's attorney) to accept papers or a complaint without having the papers served by a process server or a sheriff. Acceptance of service is accomplished by signing a "receipt and acknowledgment of acceptance of service" (or similarly titled instrument). This satisfies the notice requirement of due process.
This is cost-reducing device adopted in many U.S. jurisdictions. The defendant may refuse to accept service, but if so, the defendant will be liable for the costs of having the papers/complaint served.