Blank verse is the use of iambic pentameter in unrhymed lines, a style that Shakespeare used in his plays to show a unique character or someone who was a commoner. This style as used by William Cullen Bryant is then appropriate because he was writing for the common man, an aspect that identifies this piece as Romantic literature, where the common man was looked at as a hero.
Bryant identifies the audience in the first line when he writes that this message is meant for "him who in the love of Nature holds / Communion with her various forms" (1-2). This audience can be anyone who has a connection with Nature, no matter his station in life. Had Bryant used a very stylized form in this poem, he would not have been appealing to everyone; instead, that form is seen as connected to the aristocracy, a societal class that America was moving away from in this new country just released from Britain's grip.
In terms of the message of the poem, the blank verse also helps Bryant achieve the calming tone of the piece. Written as an elegy, a poem discussing death that moves from a somber mood to a comforting one, the blank verse makes the reader move through each line fluidly, not stopping to emphasize any rhyme that the poem might have. That fluidity aids Bryant in making his claim that one should approach death "Like one who wraps the drapery of his couch / About him, and lies down to pleasant dreams" (80-81) instead of "like the quarry-slave at night / Scourged to his dungeon" (77-78).