In general a minor is awarded as part of an undergraduate education as a recognition of the concentration of what are generally elective courses in a subject field. It usually does not constitute enough concentration to qualify one for graduate study in that field (an exception might be something like a mathematics major coupled with a physics minor being acceptable for graduate admissions to physics).
Some students elect to pursue a minor to develop a more marketable skill set, for example coupling an engineering major with a minor in business management, or a humanities major with a minor in computer science. If you go into education, a minor may qualify you to teach more subjects, similarly making you more employable. Other students simply find they have enough interest in a subject that they elect to have that recognized as a part of their degree.
Not all schools will award minors, or may have different rules for awarding them. At my undergraduate institution for example, one could not be awarded a minor in math if one majored in physics because the core courses in physics essentially met the requirements for a minor in math. Lots of other schools award this anyway.