What exactly is the core function of a business?

The "core function" of a business is its main purpose, the
most important thing that a particular business
performs.

If a business manufactures a variety of types of
appliances, its core function is to make and sell appliances. If that business makes
primarily one type of appliance, for example refrigerators, and much smaller numbers of
other kinds of appliances, you might say that the core function of that business is to
manufacture refrigerators.

If a business provides services
rather than goods, its core function is the provision of whatever service(s) it handles.
Insurance companies, for example, may provide other kinds of investments, but their core
function is the selling of insurance.

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Usually the href="http://epp.eurostat.ec.europa.eu/statistics_explained/index.php/Glossary:Core_business_function">core
business functions make up the primary activity of the enterprise, but they
may also include other (secondary) activities if the enterprise considers these as part
of its core functions.