A match box holder, openings on the sides exposed the strike area on the sides of the box. Unsure why they had the glass cover, maybe to save metal or for ornamental box-covers?
Oh, now I see. Well, something like that is usually there to allow you to put a label or ID card under the glass. There's a panel like that, made of clear plastic, in my wallet – a hold-over from the days when you could actually expect someone to return something if you lost it.