A standard website is usually designed with a desktop computer in mind as the intended device for viewing. Although it's possible to access a standard site with a mobile device, the experience for the visitor is usually not ideal, and sometimes very poor.

Mobile Options

Mobile Website - A mobile website is similar to any other website except that it is designed specifically for the smaller handheld display and touch-screen interface. Mobile websites can also access mobile-specific features such as click-to-call (to dial a phone number) or location-based mapping. As technology advances, more complex features can be delivered to phones, depending upon the type of device. Mobile sites can detect the device and deliver the appropriate experience based on the device capabilities.

Mobile Application - A mobile application is an actual program downloaded and installed on your mobile device, rather than being rendered within a browser. Mobile apps are usually sold at portals such as Apple's App Store, Android Market, or Blackberry App World and are operating system specific. The app may pull content and data from the Internet, in similar fashion to a website, or it may download the content so that it can be accessed without an Internet connection.

The most appropriate choice for your site depends on your goals. If you are developing an interactive game, an app is probably going to be your best option. But if your goal is to offer mobile-friendly content to the widest possible audience, then a mobile website is probably the way to go. In some cases you may decide you need both a mobile website and a mobile app, but it rarely makes sense to build an app without already having a mobile website in place.

Generally speaking, a mobile website should be considered your first step in developing a mobile web presence, whereas an app is useful for developing an application for a very specific purpose that cannot be effectively accomplished via a web browser.

An excellent article exploring these options further is here.