Sometimes the first page of your web site is NOT the best place for a potential client to start.
For instance, if you're advertising, either print or online, shouldn't you push your potential customer towards a page dedicated to the product they want? You don't want to send them to your home page, where they might be distracted or confused by other offerings.
A landing page is a page specifically designed around one particular idea, AND designed to push people to ACT IMMEDIATELY!
If you are doing Google Click-Thru Advertising, Print Advertising, or just about any other marketing - you need a landing page.