The Elements panel shows the HTML content attributes that are defined on an element.
jQuery plays a bit weird there - $element.data("foo") would give you the value of the HTML data-foo content attribute set on an element, but $element.data({"foo": "bar"}) will not set the HTML data-foo content attribute back on the element. jQuery keeps it in its own storage, separate from the DOM.
There are some Chrome extensions targeted at jQuery, for example (from a quick search) -
Which is supposedly adding another drawer to the side bar that shows the content of the jQuery data() of that element.