A natural language is a language that is spoken, written or even signed by humans for general-purpose communication. The term applies to a language that has evolved naturally, and the study of natural language primarily involves native (first language) speakers and refers to actual linguistic behaviour. As a consequence of this it is related to descriptive linguistics rather than linguistic prescription.
Although the exact definition may be open to debate, it is to be distinguished from formal languages - such as computer-programming languages or the "languages" used in the study of formal logic - and from constructed or artificial languages such as Esperanto.
The rules underlying natural languages are the object of study by linguists, and such study reveals much about not only how language works in terms of syntax, semantics, phonetics, phonology, etc. The study of how natural languages interact with the human brain is the field of neurolinguistics.
The theory of universal grammar proposes that all natural languages have certain underlying rules which constrain the structure of the specific grammar for any given language.