The overarching theme of "Death the Leveller" is the statement that death comes to all. "There is no armour against Fate" - nothing can be done to protect any human against the sure and certain fact that eventually that person is going to die. This idea is presented in the first stanza, which expands that statement by adding that "kings" with "Sceptre and Crown" must "tumble down" and die just like "the poor" who used "crooked scythe and spade" while living.
The second stanza continues to develop the theme. Soldiers may engage in fierce battles, killing great numbers of the enemy and winning "fresh laurels" for their honor and glory. In the end, however, the soldiers must "stoop to fate" and become "pale captives" to death in the same way that those they defeated died.
The third stanza explains the one thing of worth that may remain. All humans "must come to the cold tomb." The only thing that distinguishes one from another after death is the memory of "the actions of the just," which are pleasing reminders of the deceased.