Sonnet 55 most likely has two purposes, the most important being to insure the poet's lover that his or her beauty will outlive time and events and, less important, to claim the primacy of the written word.
The first quatrain establishes the power of the poem to make the lover's beauty remembered for all time:
Not marble, nor the gilded monuments/Of Princes, shall outlive this powerful rhyme;/But you shall shine more bright in these contents. . . .
In other words, poetry will outlive marble and gilded (surfaced by gold) monuments, and the lover's beauty will shine more brightly in these verses than monuments that have deteriorated over time ("besmear'd with sluttish time"--"sluttish" meaning "sloppy").
Not only will the lover's beauty outlive the ravages of time, but also such events as war and other conflicts will not effect the poem's ability to memorialize the lover for all time (ll.5-8).
In the third quatrain, Shakespeare takes on the most serious threats to the permanence of his lover's beauty:
'Gainst death and all-oblivious enmity/Shall you pace forth; your praise shall still find room/Even in the eyes of all posterity/That wear this world out to the ending doom.
Even death--and any other thing that would erase the lover's beauty ("all-oblivious enmity")--cannot keep the lover's beauty from being acknowledged by people of all time ("eyes of all posterity") until doomsday.
The couplet confirms the assertion in lines 11 and 12 that, until the lover is summoned from the grave on Judgment Day, the lover lives both in the poem and in the eyes of all other lovers.