Natural language: Set of symbols that can be combined into statements, questions and stories, to convey information and represent anything whatsoever that can be thought about, experienced or imagined.
There are other definitions of natural language, but one essential point about it is that it is a distinctively human gift, and is - together with mathematics, that is also at least conveyed and expressed by language - what makes human beings different from other animals. Almost everything that makes human beings specifically human rests on the skill of natural language, that any healthy neonate can pick up in a few years by being exposed to speakers of the language.
And there are several thousands of human languages, any of which can be picked up in a few years by young human children, and any of which, one it is understood, can be used to translate almost anything that can be said in any other human natural language.
Three things that far less often remarked than they should in the context of natural language are the following, all of which are of considerable epistemological and philosophical importance.
1. It takes a considerable amount of learning, talent, aptitude, skill and knowledge to learn a natural language and to use it well, in an everyday sense, and indeed this is one strong argument against many kinds of skepticism: However often one claims, with a would-be wise face, that one knows that one knows nothing, one needs to know language to claim it - and this, apart from whatever else one may or may not know, involves a great amount of knowledge and a skill that is beyond non-human animals, that seem to be unable to properly understand the idea of a symbol. And almost everything a human being may be that makes him or her human involves that linguistic knowledge, that is indeed real knowledge: True belief about how certain speech sounds are used and what meanings, intents and uses these sounds have in the community the language is spoken.
2. It takes a lot of give and take and thinking about what other people may have in mind when they say something to really understand a natural language, and indeed it seems to involve almost necessarily what I call personalism: The philosophical assumption that other human beings have experiences - beliefs, desires, feelings - like one has oneself, and that one can understand others by assuming they are and feel and desire and believe much like one does oneself. That is: Natural language and its learning involve a theory of mind that involves attributing a theory of mind to other speakers of the natural language one uses (or tries to learn), and therewith assumes other persons as existing. This is of some philosophical importance, since in actual fact the experiences of other persons are not given to one at all. (See: Qualia, Other minds)
3. There is much about natural language that is not fully understood, notably such as are related to meaning and representing and to propositional attitudes. In any case: Human beings are the linguistic animal par excellence, and owe nearly all they are and can be to their ability to communicate and think with the help of language.