Use folders to organize your cards. You can even put a folder in a folder, it's folder inception!

When you're in the Card Directory, press the big "+" button at the top of the page

Give your folder a name and then you're all set! You can also create a folder inside of a folder by pressing the + button on another folder's action bar:

You can drag and drop folders and cards inside of the card directory. Once you drag a folder, the folder will be outlined in green and then can be dropped.

When you delete a folder, all cards beneath it will not be changed. They will be moved to the top-level and marked as "No Folder".