What's he saying?
"Like as the waves make towards the pebbled shore / So do our minutes hasten to their end;"
Like waves moving toward the pebbled shore, the minutes of our lives are ticking down,
"Each changing place with that which goes before / In sequent toil all forwards do contend."
Each minute (or wave) replacing the previous one, in a continuous forward march.
"Nativity, once in the main of light / Crawls to maturity, wherewith being crown'd,"
The newborn sun rises above the sea and crawls up to maturity (noontime), where it is kingly,
"Crooked eclipses 'gainst his glory fight / And Time that gave doth now his gift confound."
But slanting eclipses challenge the sun's glory, and Time, which gave the noon sun, now clouds it over.
"Time doth transfix the flourish set on youth / And delves the parallels in beauty's brow,"
Similarly, time destroys the perfection of youth, and carves wrinkles in a beautiful face,
"Feeds on the rarities of nature's truth / And nothing stands but for his scythe to mow:"
And time feeds on the preciousness of nature's perfection, and lays waste to all in its path.
"And yet to times in hope my verse shall stand / Praising thy worth, despite his cruel hand."
And yet I hope my verse will stand the test of time, praising your worth in spite of Time's cruel hand.
Why is he saying it?
This is one of the most famous of the sonnets and perhaps the best illustration of the theme of the ravages of time. Each quatrain engages the theme in a unique way, with the destructive force of time redoubling with each successive line. Although the poet seems certain that Time's destruction is inevitable, he is nonetheless hopeful that his verse will get away with it in the end.
In quatrain one the flow of time is compared with the incessant beating of the waves against a shore, each wave building in strength and then crashing down again only to be followed by another in its place. The second quatrain uses the sun as a metaphor for human life: it is born ("Nativity") and "crawls" (like a baby) until it reaches its highest point, whereupon it is "crown'd" (with maturity) and then proceeds to fall back into darkness, or death. Line 8 concludes the metaphor with the assertion that Time both gives the gift of life and takes it away again.
This sentiment is repeated in lines 9-12, only more strongly and deeply. Time destroys the perfection of youth: he digs deep wrinkles in a beautiful face and devours the preciousness of nature in its most perfect shape - "And nothing stands but for his scythe to mow." (Time and Death each were often pictured carrying a scythe.) Nevertheless, the final couplet speaks of the poet's intention to outsmart Time himself, defying his "cruel hand" by eternalizing the fair lord in his verse. This intention has been expressed in previous sonnets; see sonnets 17-19 for examples.
Again, sonnet 60 may be the best exemplar of the theme of the ravages of time. This theme is prevalent throughout the sonnets, and it takes many different forms, sometimes referring to the destructive power of time in general, other times focusing on the effects of time on a specific character in the sonnets such as the narrator or the fair lord. The narrator seems to be hauntingly preoccupied with the passing of time and everything that it entails, including mortality, memory, inevitability, and change. He is distressed over such things that he has no control over, and at times he appears to be fighting a futile battle against time itself, just like the sun in line 7 of sonnet 60: "Crooked eclipses 'gainst his glory fight."
Finally, some scholars have suggested that the ordering of the sonnets does not in fact correspond to the chronological order of the events they describe. Could this possible rearrangement be a deliberate attempt on Shakespeare's part to defy the one-way linear progression of time? It is interesting to note that certain sonnets with "special" (i.e. time-related) numbers take up the theme of time themselves. Sonnet 60 is a good example of this: note the pun on "our minutes" in line 2 - the phrase sounds like "hour minutes" - this is sonnet 60, and there are 60 minutes in an hour. For another example see sonnet 12, which begins, "When I do count the clock that tells the time"; as we all know, there are 12 hours on a clock face. Could these just be coincidences?