In Shakespeare's sonnet, "Shall I Compare Thee to a Summer's Day?", what does "this" refer to?

Shakespeare wrote a number of sonnets in which he affirmed that the person being addressed would be immortalized in the fourteen lines of poetry because his poetry was immortal. Sonnet 18 is an example. The closing couplet reads:

So long as men can breathe or eyes can see,So long lives this, and this gives life to thee.

The word "this" in both cases refers to the sonnet itself. Shakespeare is saying that this sonnet...

Shakespeare wrote a number of sonnets in which he affirmed that the person being addressed would be immortalized in the fourteen lines of poetry because his poetry was immortal. Sonnet 18 is an example. The closing couplet reads:

So long as men can breathe or eyes can see,
So long lives this, and this gives life to thee.

The word "this" in both cases refers to the sonnet itself. Shakespeare is saying that this sonnet will live as long as humanity continues to exist. This may seem like rather an arrogant statement, but the sonnet has "lived" for some four centuries and seems likely to live for another four centuries. Meanwhile the person addressed in this sonnet continues to live in spirit within the words. We do not know who that person was, but we can sense that person's presence inspiring the poet and thereby shaping the sonnet.

In the very next sonnet, Sonnet 19, the closing couplet contains the same idea, or poetic conceit.

Yet do thy worst, old Time, despite thy wrong,
My love shall in my verse ever live young.

These sonnets were presented like individual gifts, and the recipient must have felt pleased that the poet was offering him (or her) a gift of long life or even immortality. No doubt the recipient would preserve the sonnet because it seemed to have a sort of talismanic power to protect him (or her) against the ravages of time or even death. 

Sonnet 55 has a similar poetic conceit. The opening lines are:

Not marble, nor the gilded monuments
Of princes, shall outlive this powerful rhyme;
But you shall shine more bright in these contents
Than unswept stone, besmear'd with sluttish time.

Shakespeare had a deservedly high opinion of his poetic gifts. He knew he was honoring the recipients of his sonnets, even if they did not value them as much as they deserved.