It seems that the (Zen) term Ordinary Mind can be understood in a few different ways.
It can refer to awareness being familar and comfortable with the transpersonal – or Big Mind – perspective. Big Mind is ordinary.
Big Mind & Self
It can also refer to relationship between the self and Big Mind as familar, comfortable and ordinary. Nothing special.
Living in the World
And it can refer to living in the world from a Big Mind perspective, and being familiar and comfortable with it. We appear as ordinary – as nothing or nobody special. We respond to situations as they come up, in an integrated way – from Big Mind and self. There is no need for anything extra.