Okay, so the Refine Edge box is a bit confusing....
Radius and Contrast deal with how feather works...
Smooth works about how you would expect...makes any sharp edges in your selection smoother...would bring the whole selection towards a uniform sphere if the slider was long enough...
Feather is the exact same as it was in the old dialog...
Contract/Expand work pretty much like grow and shrink....pretty self explanatory...
And the boxes on the bottom are different preview modes...there is (from left to right) Selection edges, Quick Mask view, selection on a black background, selection on a white background(used in the SS), and finally Mask view, a selection mask view, akin to viewing a pure selection channel.
And as you can tell from the 3rd pic, whenever you have any selection tool open, or quick mask, there is a refine edge button on the tool options bar.