The first key decision in a project such as this is whether to go with a native application or an app delivered through the browser. Since in this particular case the people I was writing for all used iPhones, perhaps the natural choice would have been to write a native iPhone application. They could, however, just as easily have been using Android or a whole host of other devices. The real benefit of the native application (aside from speed perhaps) is the ability to interact with the hardware on the device your application will be running on. Since I did not require access to a camera, GPS, accelerometers or any other phone features, delivery through a web browser was a very realistic option. In giving up the ability to access these hardware features you gain the ability (if done carefully) to write-once run-anywhere. That is, the application I came up with would be able to run on an iPhone and Android or pretty much any device with a web-kit based browser and a decent touch screen interface, but at the cost of not being able to use, for example, a bar code scanner.
As a bit of background (and again this is my understanding so may not be absolutely accurate) Sencha was formed by the merger of JQ Touch and the EXT JS toolkit when the original author of JQ Touch, David Kaneda, joined forces with EXT development. Essentially, Sencha Touch is the next generation version of JQ Touch but now has a small army of developers, a community, and a company behind it to provide a support network.
In the early days of my playing around with the Sencha Touch beta code I wrote a mobile version of a badminton web site I maintain. It's not particularly advanced and certainly not representative of all the things you can do with a toolkit like this but thought I'd put it out there anyway. It should, at the time of writing work with iPhone, iPad, Android and Blackberry devices and quite probably with others too. If you're trying on your desktop then make sure you're using a WebKit based browser such as Google Chrome or Safari, or for something a little bit different the great little browser Midori. For a better selection of demos take a look at the Sencha Touch Demo page and for a developer perspective on the widgets and options available in the toolkit have a look at their Kitchen Sink demo which gives a simple overview of many of the components.