Sonnet 55 is one of Shakespeare's most famous sonnets. He is simply saying that the poem he is writing to some unnamed person will last longer than marble gravestones or stone monuments decorated with gold (i.e. gilded) dedicated to departed royalty. And the individual being addressed in the sonnet will live longer in human memory because he is enshrined in the poem.
This turned out to be the simple truth, because Shakespeare's sonnet is still being read after over four hundred years, while few marble gravestones, marble markers, or gilded monuments have remained in existence for that long, having been overturned, uprooted, or destroyed by wars. And it would appear that at least some of his sonnets, including the one numbered #55, will be read for many hundreds of years to come.
The opening lines of Sonnet 55 establish a setting of a cemetery full of stone memorials of all shapes and sizes. This suggests that the person to whom Shakespeare is addressing this sonnet is dead and that therefore the poem is a sort of ode or memorial. Otherwise, if the addressee is not dead, then this kind of poetic imagery could seem morbid and offensive to the recipient.
The sonnet has a tone of both pride and humility. The speaker (undoubtedly Shakespeare himself) cannot afford a marble monument to the loved one (or perhaps is not entitled to commission such a monument), but he knows he can write poetry that will outlast the most ostentatious tombstone. (Milton in a sonnet to Shakespeare says that the poet's own works are a better testiment to his memory than a great pyramid.)
The sonnet contains one exceptionally striking and characteristically unaffected Shakespearean image:
But you shall shine more bright in these contents
Than unswept stone, besmear'd with sluttish time.
A neglected marble headstone in an old cemetery takes on a greenish-brown stained look resembliing the white stone steps in front of a townhouse which are tended by a sluttish maid who should sweep before scrubbing but only smears the accumulated dirt around with a wet mop. These two amazing lines, containing a metaphor within a simile, attest to Shakespeare's confidence in his poetic genius.