Simply explained: how does GPT work?

By now, you have probably heard of OpenAI’s ChatGPT, or any of the alternatives GPT-3, GPT-4, Microsoft’s Bing Chat, Facebook’s LLaMa or even Google’s Bard. They are artificial intelligence programs that can participate in a conversation. Impressively smart, they can easily be mistaken for humans, and are skilled in a variety of tasks, from writing a dissertation to the creation of a website. How can a computer hold such a conversation?