An LLM is a model trained on enormous amounts of text until it becomes extremely good at predicting what should come next. That sounds too simple to be useful, but at scale it produces something remarkable: a system that can write, summarise, translate, analyse, answer questions and write code.
ChatGPT, Claude and Gemini are all products built around LLMs. The LLM is the engine. The app you type into is the car built around it (see harness).
Why you keep hearing it
Because it is the umbrella term for the whole current wave of AI. When people say "the model" or "the LLM", they mean the underlying text brain, as opposed to the app, the features or the company. Debates about what "the LLM can and cannot do" are debates about the engine, not the product.
What it means for you
Two things. First, many products you evaluate run on the same few LLMs underneath, so the differences you feel between tools mostly come from what is built around the model. Second, LLMs work with language, which means marketing, the most language-heavy function in any company, is exactly in their path. That is not a threat so much as a reason to be the person in the room who understands them.