The More button opens a drop-down menu where you can access additional options for the selected device. If an option is not supported, then it is greyed out.
The first two options open pop-up windows where you can change settings specific to the device. The same windows can be accessed from the "Device Details" page (via the General tab). The settings vary depending on the device type.
The third option opens a pop-up window where you can choose to remove the device from the Home database:
This function should be used with caution as it removes all references to the device ID, but can be useful if you need to remove an obsolete device. To proceed, follow the on-screen instructions: enter confirm into the text field and then click Remove.