I'll go through each of them in plain English.
Phonegap is a set of API's to do things such as take a photo using the phones camera, use the devices accelerometer, geolocation etc..
Basically, it is a way of communicating (through javascript) between your application and the device. For example, to take a photo (open the camera) using Phonegap you would do something like:
navigator.camera.getPicture( cameraSuccess, cameraError, [ cameraOptions ] );
This is in essence no more difficult than opening the camera in a native device language (ie: Objective C for iOS), but the beauty is that this piece of code would work on multiple device platforms (there are one or two little tweaks you have to do per device, but it is basically write once and use multi platform). So that's what Phonegap is. It is a bunch of API's to communicate with multiple device platforms using the same code.
jQuery, and more specifically in your case, jQuery mobile is a javascript library used mostly in user interface design (as well as Ajax). It makes it easier to perform animations (things like an image fading in, or moving across the screen), event handling (what happens when a user clicks, hovers, focuses on, an image or button or any element). For example, look at the following piece of code:
$('.mybutton').click(function(){
$('#myelement').fadeOut(500);
});
Those 3 lines of code fade out a specific image when a user clicks on a specific button in 500 miliseconds. Short and sweet. So that's exactly what jQuery is, a library that makes creating a nice UI easier.
jQuery mobile is (as the name suggests) aimed at mobile platform development. So besides the animations and events of jQuery, it includes functionality for touch and gestures (swipes etc..), as well as a great framework for handling pages and navigation within a mobile application.
HTML5 is the latest generation of HTML which is designed to provide a comprehensive application development platform for web based content that eliminates the need for 3rd party plugins like flash or java. Audio visual playback, drag and drop, local file storage with webSQL, and of course the canvas element for advanced drawing and animation.
Basically it's just the new version of HTML which allows a lot more modern functionality.
Are you heading in the right direction? Yes, you definitely are. While learning a mobile platforms native language has its perks and is well worthwhile, a lot of developers are turning to more universal platforms such as Phonegap.
A great place to start is right here (StackOverflow), and I would definitely suggest having a good read through the documentation for Phonegap and jQuery Mobile and playing around with some of the demos.
Here are a few useful links on the subject:
Good luck and have fun