In Progress Work
This contains your current "context", what you're currently working on, your pending code changes.
This is the most interesting feature, I think. It allows you to change the context which you are working in so you can switch tasks on request.
Imagine you're deep into coding a feature and an urgent bug is raised that demands immediate attention. Your code might not even compile yet but you have to drop it and get a working setup.
Simple. Just hit "Suspend" and your current changes will be suspended. But not just your changes. This doesn't just save the current state of the source code, it saves EVERYTHING, breakpoints, watches, open windows.
When the bug fix is complete and checked in, simply drag your suspended work back into the "In Progress" section.
This very short video explains the feature in more detail.
Available Work Items
A handy query that shows all the work items currently assigned to you. This includes bugs automatically raised when your changes have broken the build. It can be filtered by Iteration and has a handy link for creating new tasks.
Perhaps most usefully, dragging a task into the "In Progress" section changes its status, which is reflected on the team scrum board.
Code reviews you have requested or received display here, and various filters can be applied. You are doing code reviews using Visual Studio, aren't you?
In short, the My Work window provides a handy at-a-glance look at your current work in progress, as well as offering the extremely useful Suspended work feature which allows you to quickly and easily take on urgent tasks without losing your context.