JQuery Mobile and Sencha Touch are JavaScript libraries that will let you create an HTML5 application that looks like a native application. Cordova/Phonegap lets you wrap your HTML5 app in native code and provides a common JavaScript API that gives you access to native functionality, like taking a picture with the camera or getting the users Contacts. Another benefit of using Cordova is that it creates native applications for you using the same HTML5 app, so you can publish these files to App stores and increase your distribution. With a JQuery/Sencha Touch only app, you can't distribute on app stores because your hybrid app is simply a website (so, I guess it'd only be a mobile app.)
There are hundreds of blog posts comparing different JavaScript frameworks like Sencha vs jQuery vs Dojo, so you should just go off and do some of that reading. Personally I would suggest Dojo as I think it is the most powerful and enterprise ready framework, but it can have a steep learning curve. One thing I like about Dojo though is the build system, you can pick and choose the modules you want so that you don't have to end up including an enormous .js file like JQuery. I have no idea if jQuery can do this, but a lot of user apps I have seen that use Cordova and JQuery end up including all of jQuery and then jQuery mobile.
If you want to access native device features and/or package the web app as a native app and distribute it on the stores, you should use one of those JavaScript frameworks in combinations with Cordova. (Cordova is the new name for PhoneGap.) Phonegap/Cordova is not really used to build mobile web apps, it's used to extend the capabilities of mobile web apps and allow them to access native device functionality in a completely cross platform way.