The whole point of nonlinear regression is to fit a model to your data. So that raises the question: What is a model?

A mathematical model is a description of a physical, chemical or biological state or process. Using a model can help you think about chemical and physiological processes or mechanisms, so you can design better experiments and comprehend the results. When you fit a model to your data, you obtain best-fit values that you can interpret in the context of the model.

A mathematical model is neither a hypothesis nor a theory. Unlike scientific hypotheses, a model is not verifiable directly by an experiment. For all models are both true and false.... The validation of a model is not that it is "true" but that it generates good testable hypotheses relevant to important problems.

R. Levins, Am. Scientist 54:421-31, 1966

Your goal in using a model is not necessarily to describe your system perfectly. A perfect model may have too many parameters to be useful. Rather, your goal is to find as simple a model as possible that comes close to describing your system. You want a model to be simple enough so you can fit the model to data, but complicated enough to fit your data well and give you parameters that help you understand the system, reach valid scientific conclusions, and design new experiments.