An anonymous call is a call made with caller ID disabled, so the recipient cannot see the caller's phone number. This is done by dialing 184 before the phone number or setting the line to always-withhold. The recipient's display shows "Withheld."
Anonymous calls have legitimate uses. Privacy protection when you don't want to share your personal number, businesses hiding employee personal mobile numbers when calling, and medical facilities not wanting to reveal direct lines when returning patient calls. Conversely, to notify your number, dialing 186 before the number temporarily overrides the withhold setting for that single call.
However, anonymous calls are also frequently abused for nuisance calls, harassment, and vishing fraud, so blanket rejection of anonymous calls is widely used. NTT's "Number Request" service (220 yen/month) automatically plays a message to anonymous callers saying "Please call again with your number displayed" and disconnects.
Smartphones can also reject anonymous calls. On iPhone, Settings > Phone > Silence Unknown Callers automatically sends calls from numbers not in contacts to voicemail. On Android, methods vary by manufacturer and model, but blocking anonymous calls is possible through the phone app settings. Note that even when calling anonymously, the caller's number is recorded in the carrier's system. If police obtain a search warrant, identifying the source of anonymous calls is technically possible. Review detailed procedures in smartphone privacy settings.