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.
Usually the 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.