API stands for Application Programming Interface. It is basically a series of commands that programmers can use to access/communicate with another program like GPT3. A kind of specialised instruction set for your program like gpt3.

Having an API connection to something like gpt3 is very similar to having gpt3 running on your own computer in a functional sense. It just means that you do not have to have the high performance hardware to run it on. It is the best option for something like gpt3 to be able to get as many ordinary people using it without us all going out and buying extremely expensive hardware.