James Shirley's "Death the Leveller" deals with themes that are quite ubiquitous now: that there is no escape from death's finality and that it is, in the end, the great equalizer. You can consider the truth of this in light of memory and remembrance.
The concept of finality is easy to understand, but the "leveller" part seems flimsy when we consider the impact of death in our daily lives. Most everyone has had someone close to them die. Some experience it with shock, others with sadness; then there are those who turn mourning into a way of life, even, refusing to ever let go. So in that way, death is permanently present, but there is little equality to be seen. The death of a family member is not the same as someone's passing being reported on the news, neither of which are the same as some great catastrophe or accident. Subtle nuances impact how we feel about each individual death.
James Shirley touches upon the ultimate death, the end that comes when not just the person is gone, but their memory as well. He says, "And in the dust be equal made." By this he means that everything material is subject to death—not just people, but all the ways they've tried to achieve immortality and remembrance, as well:
Sceptre and Crown
Must tumble down
Things, then, can experience a death of their own. Shirley's poem speaks, among other things, of the desperate attempts to shield ourselves from death. We build castles, carve our names into stone, build monuments, and write songs. We teach our history, we do everything we can to avoid the moment when we're truly and finally lost to the world. Then we "in the dust [are] equal made." His chosen symbol of dust is a good one, because it implies the kind of harsh anonymity that death eventually forces upon us all.
Then we come to the last stanza and Shirley's final thought on the matter. He believes that
Only the actions of the just
Smell sweet and blossom in their dust.
It is James Shirley's belief that in the end, there is only one thing that raises above the "levelling" powers of death, and that is being just. Only that can blossom when everything else is gone. In that way, good deeds have the potential—in the poet's mind—to live longer than anything else. Whether that is a form of immortality or not is up to the reader to decide.