"Remember" begins with simple immediacy, as the speaker addresses her listener with one straightforward demand: remember me when I'm dead. But the way she imagines her death tells readers a lot about why it's so important to her that she be remembered.
Death, to this speaker, is a country. She imagines it as "the silent land," "far away": not just remote, but speechless. No messages can travel to or from this soundless place. Where some might imagine death as a place from which they can watch over their living loved ones, this speaker frames it as a place of complete disconnection.
The anadiplosis of these first lines emphasizes the distance and disconnect of death: the speaker won't just be gone, she'll be "gone away, / Gone far away." Even the way she uses the word "gone" underlines her point. She imagines gone-ness as a state of being: she doesn't say "remember me after I go away," but "when I am gone away," as if her very self will become a vacancy after her death.
These lines make clear that the poem is an apostrophe, a direct address to someone. While the reader doesn't know who this person might be, these first lines create the strong sense that it's someone the speaker feels very closely connected to—so closely connected, in fact, that the thought that he might forget her when death separates them necessitates a whole poem!
The reader may also begin to get some hints about the addressee's identity when they notice that this poem is a Petrarchan sonnet—a form strongly associated with love poetry. (See the "Form" section for more on this.)