First, navigate to Catalog > Manage Categories:
On your left you will see all your categories and subcategories.
Find and click on the category you want to add an image to.
You will see a list of tabs to chose from:Click on Menu and change your Submenu type to Mega Drop-down:
In the same page, navigate to Category Blocks. You will see Top Block, Left Block, Right Block, and Bottom Block.
You can insert your image through the WYSIWYG Editor or by using HTML.
Click on Show/Hide Editor to fully use the WYSIWYG Editor.
How each Category Block works:
Top Block: image is displayed above the category title
Left Block: image is displayed left of the category title
Right Block: image is displayed right of the category title
Bottom Block: image is displayed under the category title