As the speaker tells us in the opening lines of the poem, the "glories of our blood and state" are shadows, not substantial things. What he means by this is that our mortal state isn't real; it's just a shadow, and a faint shadow at that, of ultimate reality, which lies beyond the grave.

It doesn't matter how much glory one achieves in one's life or how rich, powerful, or famous one becomes—death will still eventually come, as it must to everyone. This is what is meant by the poem's title, "Death the Leveller." Death brings everyone down to the exact same level, high or low, rich or poor, commoner or king. In death, everyone is made equal in the dust; in the democracy of the dead, where all are equal, there is no room for personal glory or social status or wealth, the shadows of our earthly existence.