Let not Ambition mock their useful toil, Their homely joys, and destiny obscure; Nor Grandeur hear with a disdainful smile The short and simple annals of the poor. (29-32)
The speaker seems to expect the reader—at least, rich, snooty readers—to look down their noses at the lives of the poor because they didn't accomplish anything worthy of being recorded in the history books.
Full many a flow'r is born to blush unseen, And waste its sweetness on the desert air. (55-56)
The speaker uses a metaphor, though, to point out that some of the poor people buried here might have been worthy of being recorded in history books, but never had the opportunity. They wasted their lives in the "desert air" of their tiny village and were never recognized by the wider world.
Some village-Hampden, that with dauntless breast The little tyrant of his fields withstood; (57-58)
There could have been someone like John Hampden, a man who stood up to the tyranny of the king, living in this village, only no one ever wrote down what he did. Does that make his accomplishments any less valid or legit?
To scatter plenty o'er a smiling land, And read their hist'ry in a nation's eyes, Their lot forbade: (63-65)
The speaker points out that the villagers' situation (their "lot") kept them from making a big splash in the history books. After all, they were pretty busy just keeping food on the table!
Along the cool sequester'd vale of life They kept the noiseless tenor of their way. (75-76)
The villagers had to live their lives in the seclusion of the village—outside of the national spotlight. They didn't make a lot of "noise," in that they didn't do anything that got recorded in the history books, but that doesn't mean that we should just forget about them.