In plain English
A model goes through two very different phases. Training is the long, expensive process of learning patterns from data, done once and usually on a large cluster of machines. Inference is what happens every time somebody actually uses the result: the finished model takes an input, runs it through those learned patterns, and returns an output. Every reply you get from a chatbot is one round of inference.
Why it matters
Training costs are a single large bill, but inference is charged every time anyone uses the system, so at scale it is usually inference that dominates the running cost and the energy use.
A worked example
Asking a chatbot to summarise an email is inference. The model is not learning anything from your email, it is applying what it already learned during training.
Common confusion
People assume a model learns from every conversation. It does not. Unless the provider deliberately retrains on your data, inference leaves the model completely unchanged.