Yes as Saeed says - this is the base connector for a phone cradle. When I bought my car it had a cradle attached for what I think was a Nokia 6xxx series phone attached to it.
I'd be a bit wary of trying to remove it through - I ejected the cradle to free up some space (so mine looks like yours does now with just the base plate) but if I scan my car for errors it does flag it as not having a cradle attached.
I've no idea what would happen if you then tried to further remove the baseplate from the system - possibly cause a even greater issue.