You can create both labels and folders in Airmail without the need of logging in the webmail server. 

How to create a label in a Gmail account?

Airmail allows you to create a label in your account. Please note 'New Label' feature is available only in Gmail accounts and the option will be in the 'Folders' menu only when a Gmail account is selected. In the picture below, 'Mark' is a Gmail account.

To do this you have to choose 'New Label' as shown in the picture below:

Then enter the name of the new label and choose the desired color and choose 'Done'.

How to create a folder in Airmail?

If you go to 'Folders' on the menu bar while you have selected any other type of email account than Gmail, Airmail will not display 'New Label' but will only display the 'New Folder' option.
Please see the picture (the selected account is not a Gmail account) below:

Then enter the name of the new folder and choose the desired color and choose 'Done'.

How to create a Subfolder in Airmail?

Please right click any folder/label (for which you want to add a subfolder) and choose 'New Subfolder' - OR - Select the folder and then go to Menu Bar > Folders and choose 'New Subfolder'.

The first method is shown in the picture below.

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