"Where is this panel going to exist in the ListBox?" - The listbox will make one copy of it for each list item, i.e. one for each element in the myTodoList collection. So within each list item, you'll have the three labels stacked one above the other.
"What is its purpose in the ItemTemplate?" - To make it possible to show more than one control for each element in the ItemsSource. ItemTemplate, like many things in WPF, can only take one child element, so if you want multiple children, you need to specify how you want them laid out, and you do that by adding a panel (StackPanel in this case).
"Can any System.Windows.Controls.Panel be used in its place, specifically a Grid?" - You bet.
"How would I go about using a <Grid> element as the template for each item in the ListBox?" - The same way you would use a Grid anywhere else. It's no different; it's just that ItemsControl (and its descendant, ListBox) will create multiple instances of your Grid. Note, though, that inside the ItemTemplate, your DataContext will be the current list item, and therefore your {Binding}s will be relative to that list item (unless you specify otherwise with e.g. ElementName).
"Does this look correct?" - This really should be posted as a separate question, as it's unrelated to the questions about the MSDN sample, and I'm not even sure what you're trying to do. But I'll try to answer: I suspect something is wrong, because you're using the name "GraphLabelYData" two different ways. In the ColumnDefinition, as far as I can tell, you're treating GraphLabelYData as the name of a XAML element (i.e. you're looking for another control in the window/page/UserControl with Name="GraphLabelYData" or x:Name="GraphLabelYData", and reading that control's GraphLabelMarkerLength property); but in the TextBlock, you're treating GraphLabelYData as the name of a property on the current collection item. I suspect one of those isn't right.