Breaking down the Wave Gen 1 app from the top down:

This is your Menu, here you can access your device settings, app settings, account information, shop, contact support or view the Airthings Help Center
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Is how you add your Airthings Wave, Wave Plus, Wave Mini, or Hub to the Airthings Wave App.
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Is only applicable to Airthings Hub users - Once you add your Airthings Hub to your account in 2. you can choose to link your Airthings Wave, Wave Mini, Or Wave Plus to your Airthings Hub by choosing this linking button. If you do not have an Airthings Hub on your account you will not see this linking icon.

This is for Airthings Hub users only, here you can find the serial number of your Airthings Hub or choose to link any non-linked devices from within the menu.
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Location Name followed with the sensors below in that location. If you have more than one location, it will be separated from a new location name and the sensors assigned to that location below.
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The color ring indicator: this is an overview of the color ring status for each device from the last time it has synced. If the status is "Up to Date" this will match the color ring on your Wave, Wave Plus, or Wave Mini. If the status is not "Up to date" this will reflect the color ring based on the last time you synced with your monitor.
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Room Name
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Airthings monitor model
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Syncing Status
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SmartLink signal strength for Airthings Hub connected devices only