Note also that if you hit the "{whatever} Slot" button next to the socket on that screen it will give you a pull down list of every valid gem you own for the socket, including ones that are back in your bank. I found this pretty handy once I figured it out.
I find this game cycles me fairly constantly between fun and frustration, most of the latter with the insane decisions they made in the interface. For instance, if you have the bank open you can still activate right click menus on items but selecting an option puts it in the bank anyway. Also double clicking on an item in the bank sends it back into the bank instantly, rather then to your inventory, which is I think unique to MMO bank design.