Google's plan for the "Photos" gallery does not include placing images into separate folders, although it will recognize folders that you create outside of the app. So, for example, you could use a file manager app to create folders within the default images folder or outside of it - either way, the Photos app will find them.
The Photos app itself gives you the ability to create "Albums" and assign images to them. As near as I can see, these albums are not physical objects (as in actual folders/sub-folders), but simply classifications which can then be assigned to individual images. As such (again, from what I can see), a single image can be a part of multiple albums without making multiple copies. An advantage to the Albums system is that an individual album can be shared to friends or family.
If you prefer to put images into folders and want to manage them without resorting to using a file manager, there are numerous gallery apps available in the Play Store, at least some of which support folder management.