When you are in a meeting, at the gym, ran home to pick up the sandwiches you made but forgot to put in your bag, etc., you might set your answerphone to tell callers why you're not answering, instead of the usual "I'm not available to take your call, please leave a message". However, you might not want
any and every caller to hear that you are in the gym, or in a meeting - it's either information they shouldn't know, or just don't need to. At the same time you really really want your loved one or your boss to know that you're not avoiding them or avoiding work. Solution: the auto textback. [and it just occurred to me that there may be a way to have a different answerphone message for different numbers, but I'll leave that aside for now]
When you are not answering, and have set your phone to divert to voicemail, auto text back is a feature which allows your phone (or more likely its network) to *not* divert selected numbers (e.g. your partner, your boss) through to your answerphone. Moments later, it sends them a short text message, something you pre-wrote like "I'm not answering because I'm at the gym on my lunch hour - I'll be out at 2.30pm, so call me back then if you need to. Thanks." If it's urgent, they'll call you back. If it's really urgent and they need you before 2.30, they'll call the gym (yes, they would have done if that was on your voicemail message, but all sorts of other people who went through to your voicemail didn't need to hear your location, did they...). And if it wasn't urgent, well, they know where you are and they know when you'll be available.
clearly this requires caller ID in order for the service to know to whom it should textback; if in doubt, it would put the caller through to regular voicemail. If the caller ID is a normal office phone which can't accept SMS/text messages, the message can be sent as an email or pager text - this is a bit more elaborate but I know it is possible with present technology.
[just noticed another person's idea from a few days ago 'activity related voicemail' and realise that this is similar. To get my pleas against redundancy in early, I should say that setting up ten different voicemails takes longer perhaps than writing short text messages. The other advantage is that when you are busy, your caller doesn't need to wade through messages and choose which one applies to them, all the while it costing money for them to listen to you on your answerphone - with my idea they don't spend any money, but it costs you a few pence to send the text to them.]