Shakespeare compares his loved one to a summer’s day and other beautiful aspects of nature. He categorizes objections to nature’s beauty in favor of enduring depictions of the one he loves. The summer day eventually ends and summer eventually leads to fall, winter and unharmonious weather. The speaker transitions from objections to nature to his praise of his loved one. She (or he) does not have an earthly immortality. But writing allows the possibility of immortality. The speaker writes to preserve the memory of his loved one and this kind of immortality endures as long as there are others to read.
So long as men can breathe or eyes can see,
So long lives this and this gives life to thee.
The loved one lives on in the sonnet. Summer fades, the sun dims and humans are mortal. But writing is an art form that preserves memory indefinitely, or as long as humans and reading/writing exist. This idea of immortality through writing is almost as old as writing itself. The idea of writing is to represent, communicate and preserve meaning.