Welcome to Android Central! Use a file manager app (the stock one or a 3rd party one like ES File Explorer) to create a new folder anywhere in the directory structure. To make it easier, I suggest making it a subfolder of the Pictures folder. Then move whatever photos you want to the folder. When you open the Photos app, swipe in from the left, and tap "On device." You'll see your new folder there.
The Albums option in the menu is for your Google+ Photo albums in the cloud, not for local folders.