The emphasis should be on "general". The easiest way to understand this is by thinking of the opposite: we can already build AI systems that are very good at one specific task: folding proteins, playing Chess, detecting cats in images, translating from one language to another, detecting market inefficiencies...etc But a human, the same human, can do all those things. A human has a sort of general intelligence. This is the goal of AGI. One can think of it as a some kind of unification theory for AI systems. One model that can be capable of excelling at vastly different tasks.

AGI has nothing to do with surpassing human intelligence. However, the idea is, once you have a general intelligence running on a computer, you could easily scale it to create a super human level intelligence.