A natural language is the kind which we use in everyday conversation and writing. For example English, Hindi, Chinese. Natural languages are always very flexible, and people speak them in slightly different ways.
There are some natural languages which are simplified, such as Basic English and Special English.
An artificial language is quite different, as it is built for some special purpose. They are always very precise, and must be used according to pre-set rules. Symbolic logic, mathematics, programming languages.