I'm trying to remember the grammatical term used to describe this part of speech. The term "prepositional phrase" comes to mind, but I think it might be something different. It's the part of a sentence that introduces the sentence and gives context, but grammatically it can always be removed and the sentence will still be valid. Examples:
Being in jail, he is unable to attend.
The car having two doors, there wasn't a third one to open.
The store being closed on weekends, he would have to wait until Monday.