A great question! I realized that it is probably a much more common one than we may realize. Many of us may not even realize the true difference even though we are somewhat familiar with both.
According to Wikipedia, Marketing is "the activity, set of institutions, and processes for creating, communicating, delivering, and exchanging offerings that have value for customers, clients, partners, and society at large. Marketing as a whole is focused on acquiring, analyzing, maintaining, and generating the interest of customers.
Advertising, according to Wiki, is a form of communication used to persuade an audience (viewers, readers or listeners) to take some action with respect to products, ideas, or services. Advertising (for the intent of this blog) is used to convince consumers to invest their time and money in a certain product or service. It is a service that is paid for and made possible via various media outlets such as TV, radio, mail, and the Internet.
A fundamental difference between the two is that marketing is an overall process and/or plan, while advertising is only one piece of that plan. About.com provides a great explanation, suggesting that we visualize marketing as a pie, and advertising as one slice out of that pie.