A picture says more than a thousand words. A reference image can help you better describe how you'd like your photos to be edited.
For example: If you want to edit your hair color to be similar with the hair color in "taylorswift.jpg", then you upload it and click the "Set for reference" button to make it a reference image. Then, in the additional instructions, you can write something like "make my hair color like in taylorswift.jpg".
Another common usage is: if you want to take something out from photo #1 and merge it with photo #2, you can set photo #1 for editing, and set photo #1 as a reference image.
One more thing, you do NOT need to pay anything for reference images.