Index cards are a folder, or substorm, containing other stickies and ideas inside of it. When you delete your index card, you are deleting all of the data inside of it too.
Clicking once on the top bar of the Index Card and clicking "delete" in the pop-up menu will delete your sticky note.
Deleted index cards and the stickies inside of them can be recovered from your trash if there was a mistake.
Also see:
How do I create an index card/substorm?
How do I add stickies to index cards/substorms?