@dlowan,
Mobile platforms come with extreme usability challenges when it comes to display and input. With their tiny screens, and clumsy keyboards they found very little use as mobile computers and "smartphones" (think computer + phone) were mainly for geeks and corporate users.
There are three popular devices that have long been expected to converge into one: cell phone, music player, and pda (to make it simple, there's also digital camera as a main component in some Asian countries). The cell phone is what is expected to be the all in one device, but poor usability hampered its adoption. Most of the other smartphones out there were absolutely horrible in terms of usability and didn't see mainstream adoption.
The iPhone changed that by making a phone that solved the input and screen size problem elegantly by using a large touch screen, and by making a more usable UI that makes using your phone as a music player or a browser much less of a pain than previous mobile operating systems did. They also managed to get good battery life even while using a much more powerful CPU than most mobile devices use (CPU power tends to drain battery, so most mobiles are underpowered and thusly slow and sluggish).
But the iPhone is a proprietary and closed system from Apple, and while the Google-developed Android phones have yet to produce a hardware design that outdoes the iPhone the fact that their software is open source means that they are likely to be the more robust platform in the future.
What these phones, and their imitators represent is an effort to make mobile computing mainstream.
So if you like to browse the internet away from computers, or listen to your music, or check your email, or get GPS directions, or take photos, or have all your contacts available and synchronized on your phone and your various computers then these phones are good options.