Cognitive science is a pretty large field, but three questions have been driving a lot of the research effort, almost from the start.
What is language ?
First notice that it is a two-faced coin, there’s external language and internal language. Everybody knows what external language is : it is that particular set of sounds and signs whose shapes and sequences convey some conventional meaning. This convention is formalized into rules, exceptions and templates, and examplified in googles of more or less beautiful instances in everyday life.