The speaker addresses a listener who is deeply respected and loved. We do not learn much about the “you,” except that the relationship with the speaker is a close one. The “you” and “your” pronoun referring to the unnamed listener occurs six times in the poem.
The powers of destruction mentioned in the poem are “sluttish time,” “wasteful war,” “broils,” “Mars his sword,” “war’s quick fire,” “death,” “all-oblivious enmity,” and the collective forgetfulness of “all posterity.” The speaker claims that his own poem (“powerful rhyme,” line 2) will survive all destruction, because even though people, buildings, and institutions perish, the language will live on, and the poem is important enough to attract endless future interest.
The “living record of your memory” of line 8 refers to the poem itself, Sonnet 55. The idea is that even though the listener is unknown to readers, the “living record” still exists and the listener also therefore exists.