Mobile Web Design is the process of designing a website specifically for the mobile market. More commonly though, it is the process of re-rendering your existing website (or new website being built) so that it displays properly on a mobile device.
Amazon.com have a good example of a mobile version (see image right). The page has been compressed from a full screen 1024x768 experience to a flexible width version.
You've got to remember your audience. If you're using your mobile, it means you're not at a computer desk! You're out and about - on the train, in a waiting room or on the loo. The two key factors to take into consideration when designing for mobile are usability and time.
Users of mobile devices with touch screen technology are going to be using their thumbs when they click on a link. This means, larger buttons are going to be more easily selected than smaller ones.
A mobile user will generally have less time to spend on your site than a desktop user. This means, they need to get to the answer / reason for being there faster than a regular internet user. There are two things to focus on - reduced content (allowing each page to load faster on the sometimes lethargic G3 network) and the number of clicks needed to get a result.