The central theme of "Remember" is remembering. Rossetti explores remembrance after death through two perspectives: the perspective of one who loves and is left behind, after "darkness and corruption" consumes the beloved in death, as well as through the perspective of continuing, or immortal, remembrance.
The poetic speaker, not assumed to be the poet, requests that her beloved remember her when she is "gone far away" into death. She acknowledges that human will cannot resist the distractions of living--whether of productivity, trouble or pleasure--and counsels "do not grieve" when he forgets "for a while."
The speaker then presents a novel twist on the conventional theme of attaining immortality--or attaining continuing remembrance--through the words of poetry, which escape the ravages of death: words of poetry are what death leaves. The poet's words are the "vestige of thoughts" that are left behind by the "darkness and corruption" of death.
These words, or vestiges of thoughts, remember the poet continuingly as they are read--or even as they are simply saved though perhaps never read again, though of course Christina Rossetti is read again and again and again and is continuingly remembered for her thoughts though in "the silent land."