What is the "Attention Is All You Need" paper and why did it change everything about AI?

In 2017 eight Google engineers published a paper with a provocative title that most people outside machine learning had never heard of. Seven years later virtually every major AI system in the world, ChatGPT, Claude, Gemini, BERT inside Google Search, runs on the architecture that paper introduced. What did "Attention Is All You Need" actually propose and why was it such a radical departure from how AI language models worked before? What is the attention mechanism in plain language and why does it solve problems that the previous generation of language models could not? What is a Transformer and why did it scale so dramatically better than anything that came before it? And what is the extraordinary irony that Google published this architecture openly in 2017 and then watched OpenAI use it to build ChatGPT, a product that now threatens Google's core search business?