Finance is a very professionally oriented major designed to prepare you for a career in financial management, which is the art and science of managing money or, if you like, the way people, institutions, markets, and countries generate and transfer wealth. It's a good major and potentially a very lucrative one because, these days, everybody - small businesses, monolithic corporations, charities, and governments - needs effective financial management.
If you major in Finance, you'll study things like commercial and investment banking, forecasting and budgeting, and asset and liability management. You'll learn more than you may ever want to know about money, stocks and bonds, and how markets function. You'll learn how to determine what fraction of a firm's assets (or your own assets) to put into different kinds of investment vehicles in order to obtain the highest return for a justifiable level of risk. When you graduate, all those baffling indexes at the back of the Wall Street Journal will make sense to you.
Upon graduation, your career can take many paths (naturally), but most Finance majors find jobs in the finance departments of firms; with banks, mutual funds, and other kinds of financial institutions; or in government or some kind of charitable organization. Some schools offer specialized areas of concentration within the Finance major as well - in insurance and real estate for example.