In order to help you answer your question, I would first of all like to point out that the poet reminds his readers through this poem, "Death the Leveller," that death will ultimately come to everyone, as nobody is immune to it. The poet explains in this touching poem that it simply doesn't matter whether someone is rich or poor. Death is simply inevitable for everybody, regardless of who they are.
This is where the answer to your question can be found. The poet tells us in the first line of this poem that
The glories of our blood and state
Are shadows, not substantial things.
Obviously, it goes without saying that the word blood is is not to be taken in its literal sense. Instead, the poet uses it as a metaphor for a person's social background and social status. You might have heard that members of a royal family, for example, are often referred to as being of "royal blood." This means that they come from a family line that is linked to kings and queens.
This is what the poet refers to with the word "blood" in his poem: a person's family line, their heritage and social standing. In other words, it doesn't matter if a person comes from a rich background or a poor background, whether they come from a working-class background or whether they are a member of the social elite. As far as death is concerned, all men are equal, and death will come to find everyone eventually. As the poet says himself, "Death lays his icy hand on kings."