Corporate Finance in its most simple definiton is the area of funding for a corporation. This comes in many forms as do the needs of any one organization. The biggest, publicly-traded companies have whole teams to figure out the financing they need for short-term purposes (inventory purchases, payroll), medium-term financing (for project investments with a finite timeline, for example) and long term financing (usually for hard asset purchases such as property). Each of these categories have several different ways for corporations to tap into this financing. A CFO's job is to determine the best way to borrow these funds and then the best way to deploy the borrowed assets.
Smaller companies also have a need for financing though there are many fewer sources. Loans from commercial banks, private lenders and potentially a government body designed to aid small companies are among the few choices. Generally the owner will provide a majority of the financing at the beginning stages of the company before they are able to even get these few sources. Their borrowing rates are generally higher than big borrowers.