What does Corporate Vice President mean? Why not simply use Vice President?

Answer 1

That's because in a very large MNC, you can have one VP for each function or product line, for e.g. one for home products and one for industrial products; or they can be divided along geographical lines. In this day of globalisation, you can have a VP for the Americas, one for Europe, and one for Asia-Pacific. Or as in your example, one for Corporate affairs, maybe one for corporate communications or public relations, one for sales and marketing, etc etc.

Answer 2

It means "I am more important than just a mere VP and therefore I deserve more money"