It is the recognition that we are all one. Not that we should try to be one or hope that some day we can get together and act like we're one.
In much of traditional Christianity we've managed to quiet that troublesome emphasis by stressing the idea of individual salvation over everything else and looking at the unity concept as an interesting metaphor, or worse, as a command to act as though we were all one.
And I think (or pray) we are all one. I am no better, no more worthy, than that enormously heavy man across the aisle or that woman who recently left her husband or that child with cerebral palsy two pews in front of me.