In the first quatrain, Shakespeare compares life to the seasons, particularly growing older to fall/winter. In the second the metaphor changes to comparing one's life to the course of a single day, with "death's second self" being sleep at the end of that day.

These lines refer to death being akin to the night. There are three images in this sonnet to pay attention to: fall, twilight, and embers. All three are reflective of the process of aging.

The lines you are inquiring about read: In me thou seest the twilight of such day / As after sunset fadeth in the west,/ Which by and by black night doth take away, / Death's second self that seals up all the rest.

Line 5 "the twilight of such day" refers to getting older. The sun rises in the east and sets in the west. Therefore, the speaker is addressing the eclipse of life.

Line 8, "Death's second self" is also in reference to the dying process; "seals up" means encloses, as in enclosing life. Death will finally "seal up" all that we have experienced and endured in life.