How are music and culture connected?

The easiest answer to this is that music is part of a society's culture. 

The term culture refers to the accumulated body of knowledge and traditions possessed by a society. While not every person in a society will be familiar with all aspects of a society's culture. In the aggregate, culture is what a society teaches its children and hands down to future generations. It is what binds a society together with shared bonds of customs and knowledge and ways of thinking. 

Performance is a means by which a society shares its culture among its members. Even purely instrumental music can be a shared bond among members of a society, as in Beethoven's Ode to Joy, which for many people expresses the spirit of the European Union, even if unaccompanied by the words of Schiller.

Musical performance can often convey a society's traditions to people who are not literate, as is the case with traditional bardic performance.