If your ExpressionEngine install is using 'Assets' for asset management you have the ability to add subfolders to further refine how you organized your site images and files. Please feel free to contact us to find out if your site is using Assets or how you can migrated to this amazing asset management tool.
Assuming that your site is using the Assets tool - here are instructions for making subfolders.
1. Navigate to the Assets landing page.
2. In the 'Assets folders' section on the sidebar, right-click on the folder you would like to add a subfolder to and select 'New subfolder'.
3. In the new 'New subfolder...' window, enter the name of the new subfolder.
4. Click 'Ok'.
5. Your original folder should now have a dropdown arrow next to it. Click this arrow to view your new subfolder.
You're now one step closer to better organizing your files in ExpressionEngine. As long as the developer of your website didn't give you any "don't touch this directory" instructions, you should be able to drag and drop files between folders without worry about breaking anything on the front-end. Have fun!