In "Sonnet 18" Shakespeare declares, following the tradition set by many poets during the Classical Age, that poetry is immortal. The beauty of the young man will live forever because the poetry that describes the young man's beauty will last forever. Shakespeare returns to the idea that poetry will outlive the ravages of time despite mankind's destructive ways in several sonnets: 55, 60, and 65.
In "Sonnet 55" the speaker asserts that poetry ("rhyme") will last longer than statues made of marble or monuments made of gold or brass. Thus, the beauty of the young man will last longer in a poem than it would if it were copied into a statue or onto an engraving of some sort. Stone statues become worn away over a long period of time. And during times of war (personified by Mars -- in line 7
-- the Roman god of war) many statues and other forms of art become destroyed. When a statue or a painting becomes destroyed, the beauty of that particular piece of art is lost forever. But if a piece of paper containing a poem is destroyed, the countless hundreds or thousands of copies still remain. Thus, the beauty in a poem is immortal. Its contents can also be recopied or reprinted, and the copy is as perfect as the original. A copy of a statue or painting, on the other hand, is just a copy. Something of the original becomes lost in the process.