For some, it's simply Artificial and Generally Intelligent(perform many tasks, adapt). For some, it might mean any that it needs to do everything a normal human can. For some, non-biological life axiomatically cannot become AGI. For some, it must be "conscious" and "sentient".
For some, it might require literal omniscience and omnipotence and accepting anything as AGI means, to them, that they are being told to worship it as a God. For some, it might mean something more like an AI that is more competent than the most competent human at literally every task.
For some, acknowledging it means that we must acknowledge it has person-like rights. For some it cannot be AGI if it lies. For some it cannot be AGI if it makes any mistake. For some it cannot be AGI until it has more power than humans. These are several definitions and implications that are partially or wholly mutually conflicting but I have seen different people say that AGI is each different one of those.