Voicemail is the system that answers your phone when you cannot, and lets the caller record a spoken message for you to hear later. The word covers both halves of that: the system itself ('Our office has voicemail'), and one individual message ('You have three voicemails').

It is normally uncountable when you mean the service — 'leave a message on my voicemail', 'check your voicemail' — but people freely count the messages, and 'three voicemails' is completely normal English now, whatever older dictionaries say.

It also works as a verb, mostly in American English: 'I voicemailed him about it.' That sounds casual and a bit business-y.

Worth knowing how it has changed. Voicemail was very important in the 1990s and 2000s, when it was often the only way to reach someone who was out. Today many people, especially younger people, never listen to their voicemail at all — they see the missed call, and text back instead. Some people even record a greeting saying 'don't leave a message, just text me'. So if you leave a voicemail for a friend, you may be waiting a long time. For a company, a doctor's office, or a landlord, it still works perfectly well.

One older word for the same idea, still used for the machine on a desk: answering machine (答錄機).