To move content into a folder first select the item (section, image, snippet, or fee) by clicking the checkbox next to it. From there, click and drag the item inside the folder you would like it added to. Here's a GIF demonstrate:
You can also batch-select and move items by clicking and dragging, or using shift+click:
IMPORTANT NOTE: If you’re moving this to a folder with permissions set to "waterfall on", the permissions in the folder you’re moving will automatically change to this waterfall setting. Make sure the accesses are matching what you need before you move these in.