Talking directly to his beloved, the speaker begins with some confident words of assurance: no other memorials, however beautiful or permanent, can outdo this sonnet, which will live longer and shine brighter. Other human creations have to deal with time and violent war, but this poem escapes both of these downers.
And because this poem is a poem of praise, preserving the memory of the beloved's beauty and all-round rad-ness, there's good news: the beloved will also escape destruction. In fact, he will live comfortably inside the sonnet and the minds of readers until the end of the world itself. In other words: Don't worry, hon, I've got this.