1) My stations - which contains all of your airports / weather stations.
2) Nearby - which always contains an auto generated list of nearby stations.
3) Not grouped - which contains all of your stations which are not part of a custom group.
To create a new custom group you may touch the folder icon at the top.
To edit your custom groups, i.e. to sort or delete them touch the pencil icon at the top to enter edit-mode. When in edit mode each group will have a drag handle to move it up or down within the list of custom groups. Each group will also have a trash can icon next to it's name to delete it. When you delete a custom group you will be presented with a choice to what shall happen to your stations within that group. These can either be moved to the "Not grouped" group and remain in the "My stations group" or be deleted as well.
Also while in edit mode there is a "AZ" icon at the top. You may touch it to sort your custom groups alphabetically.
When you are done, leave edit mode by touching the check mark icon at the top.