In the first stanza of the poem, the speaker describes a woman who lived in a remote place, "besides the springs of Dove." The River Dove is in the Peak District in England. The speaker says that there was nobody to "praise" the woman, "and very few to love" her. In other words, this woman lived a solitary and quiet life. She had nobody to praise her and "very few" people who loved her. The implication is that she deserved more praise and more love than she was given.
In the second stanza, the speaker says that the woman was "A Violet by a mossy stone" and "a star when only one / Is shining in the sky!" These naturalistic metaphors suggest that the woman was very beautiful. She was more beautiful than the average woman, as a "Violet" is more beautiful than a "mossy stone." The metaphor describing her as a "star" also implies that she was, at least to the speaker, a ray of light in an otherwise dark world.
In the third and final stanza, the speaker emphasizes the impression that the woman lived a solitary life when he says "she liv'd unknown." He then says that "few could know / When Lucy ceas'd to be." Here, then we learn that this woman (who we now know was called "Lucy") has died, and we know too that her death went largely unnoticed.
In the last two lines of the poem the speaker exclaims, "she is in her Grave, and Oh! / The difference to me!" The point here is that while this woman may not have meant much to many other people, she meant a great deal to the speaker. In the final line, the speaker suggests that even though Lucy's life and death seemed to make little difference to most people, to him they made a very significant difference.