Android is an open mobile phone platform that was developed by Google and, later, by the Google-developed Open Handset Alliance. Google defines Android as a "software stack" for mobile phones.
A software stack is made up of the operating system (the platform on which everything runs), the middleware (the programming that allows applications to talk to a network and to one another), and the applications (the actual programs that the phones will run). In short, the Android software stack is all the software that will make an Android phone an Android phone.
Now that you know what Android is, let's talk about the important stuff: Why should you care about Android?
First off, it's an open platform, which means that anyone can download a software development kit and write an application for Android. That means that--eventually--you should have plenty of Android apps that you can download to your phone. If you like Apple's App Store (one of the most raved-about features of the iPhone), you should be pleased with Android.
Google has a very good reputation when it comes to creating software. The company's Gmail service, its online suite of applications, and its Chrome browser have, for the most part, been favorably received. Google is known for creating simple, straightforward applications that are inherently usable. If the company can translate that success to the Android platform, users should be pleased with what they see.
While the software will come from Google--and anyone who chooses to write applications for Android--you will have some choice in both hardware and cellular carrier. This is where Android differs sharply from the iPhone. The iPhone hardware is made by Apple, and your cellular carrier is AT&T (unless you jailbreak your phone, and therefore void any warranty). An Android phone can be made by anyone and made to run on any network. T-Mobile is launching the first Android phone, but it won't be the last; Sprint is already rumored to have an Android phone in the works, too.
These are just a few of the reasons why Android has the potential for huge success. Now we have to see if it can live up to the hype.