Fine-tuning takes a trained model and continues its training on your material: hundreds or thousands of examples of the inputs and outputs you want. The result is a modified model that behaves your way by default, without being told each time.
Here is the important part: most people who say they want fine-tuning do not need it. There are three ways to make AI behave your way, in rising order of effort. Instructions: write what you want in a system prompt or custom GPT. Retrieval: give the model your documents to answer from (see RAG). Fine-tuning: actually retrain it. The first two cover the vast majority of business needs, including "make it write in our brand voice". Fine-tuning is for high-volume, narrow, repeatable tasks where the first two fall short.
Why you keep hearing it
Because "we fine-tuned an AI on our data" sounds impressive, so the phrase gets used loosely for things that are actually instructions or retrieval. Vendors like the word for the same reason.
What it means for you
When someone proposes fine-tuning, ask the deflating question: have we already tried good instructions and good context? If the answer is no, you have found budget savings.