The term natural language is used to distinguish languages spoken by humans for general-purpose communication from constructs such as computer-programming languages or the "languages" used in the study of formal logic, especially mathematical logic. In the philosophy of language, the term ordinary language is sometimes used as synonymous with natural (as opposed to mathematical or logical) language. Natural language is also considered a field of weak artificial intelligence.
Additionally, the indigenous signed languages of the world merit inclusion as natural languages owing to extensive linguistic analysis in the latter 20th century confirming their unique and consistent grammar, syntax, rules and visual logic dramatically unlike the spoken languages of the nations or geographic regions in which they arose. American, French, and British Sign Languages are the best documented examples in the literature.
Humans have also invented (or arguably in some cases discovered) many other languages, including constructed humanlanguages such as Esperanto or Klingon, programming languages such as Python or Ruby, and various mathematical formalisms.
Humanlanguages are usually referred to as natural languages, and the science studying them is linguistics.
One should be careful about the underlying classification principle for groups of languages which have apparently a geographical name: besides areal linguistic units, the taxa of the genetic classification (language families) are often given names which themselves or parts of which refer to geographical areas.
Language is a complex, specialized skill, which develops in the child spontaneously without conscious effort or formal instruction, is deployed without awareness of its underlying logic, is qualitatively the same in every individual, and is distinct from more general abilities to process information or behave intelligently.
The view of language that suffuses public discourse — that people assume both in the sciences and in the humanities — is that language is a cultural artifact that was invented at a certain point in history and that gets transmitted to children by the example of role models or by explicit instruction in schools.
They've suggested that language appeared as a by-product of the laws of growth and form of the human brain, or perhaps as an accidental by-product of selection for something else, and they deny that language is an adaptation.
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