An Android phone is a smartphone running on Google's open-source Android operating system. Many different manufacturers make Android phones, including HTC, Motorola, and Samsung. Dozens and dozens of different Android phones are now available, and all of the major cellular carriers in the U.S. offer Android phones.
Originally derived from the Linux desktop operating system, Android is a customizable platform that can look and feel very different on very different handsets. That means that an HTC Android phone will look and operate differently than an Android phone made by Samsung. It also means that an HTC Android phone from T-Mobile won't be exactly like an HTC Android phone that runs on Sprint's network.
Still, all Android phones do share some common features. All of them have touchscreens. Some also have hardware keyboards, but not all of them do. All come with a desktop that is made up of a certain number of screens (some Android phones have 3, others have 5, while still others have 7) that you can customize to your liking. You can populate screens with shortcuts to apps or widgets that display news headlines, search boxes, or more.
All Android phones also offer access to the Android Market, where you can download Android apps. As of this writing, more than 150,000 apps are available in the Android Market.