What's he saying?
"From fairest creatures we desire increase / That thereby beauty's rose might never die,"
We want the best-looking people to have children so that their beauty can be appreciated by future generations,
"But as the riper should by time decease / His tender heir might bear his memory:"
For once the elder has passed away, his young will share the memory of his ancestor's beauty (and may look like the elder):
"But thou, contracted to thine own bright eyes / Feed'st thy light's flame with self-substantial fuel,"
But you, obsessed with your own beauty, selfishly consume all of that beauty's light,
"Making a famine where abundance lies / Thy self thy foe, to thy sweet self too cruel:"
Depriving the world of that beauty when there is plenty to be had by all; you are your own enemy, you are cruel to your own sweet self, for not having a child to carry on your memory.
"Thou that art now the world's fresh ornament / And only herald to the gaudy spring,"
You who are now a beautiful thing on earth, and the one who announces the coming of spring,
"Within thine own bud buriest thy content / And, tender churl, mak'st waste in niggarding:"
Are burying your self-satisfied beauty within yourself, and wasting it by being selfish.
"Pity the world, or else this glutton be / To eat the world's due, by the grave and thee."
Have pity on the world and bear a child; otherwise you are a glutton, keeping your beauty to yourself by taking it with you to the grave.
Why is he saying it?
Sonnets 1-126 comprise the first unit of Shakespeare's sonnets, although the second unit is considerably smaller, comprising only 28 sonnets. We often call sonnets 1-126 the "fair lord sonnets" because they tell the story of the poet's growing affection for (and eventual rejection by) a young and beautiful man that some critics also describe as the poet's financial benefactor. Almost all of the fair lord sonnets are addressed directly to the fair lord himself, and those that are not are surely about either him or the effect he has on the poet's emotional state.
Sonnets 1-17 are sometimes referred to as the "procreation sonnets," for in these sonnets the poet pleads with the fair lord, begging him to have a child so that his beauty may be passed on for future generations. This mini-theme of procreation continues until sonnet 18, whereupon the poet seemingly abandons it in favor of a new course. From then on the poet seeks to eternalize the fair lord's beauty in the lines of his verse, a plan he foreshadows in some preceding sonnets, e.g., "But were some child of yours alive that time / You should live twice; in it and in my rhyme" (sonnet 17).
From the beginning the poet appears infatuated with the fair lord's beauty, as the fair lord is infatuated with it himself. Knowing that Shakespeare often drew on Greek and Latin myth and legend in his works, we see a possible allusion to the story of Narcissus in the fair lord's obsession with his own appearance. The fair lord seems not only obsessed with his own beauty but also immoderately selfish with it - at least in the eyes of the poet. The selfishness of the fair lord with respect to his beauty is alluded to elsewhere in the procreation sequence, e.g., "Unthrifty loveliness, why dost thou spend / Upon thyself thy beauty's legacy?" (sonnet 4).
This first sonnet introduces the reader to a number of the sonnets' recurring themes: a possible homoerotic undertone (a man's appreciation of another man's beauty), the imagery of financial bondage (as in "contracted"), and the theme of selfishness and greed embodied in the fair lord's unwillingness to eternalize his beauty himself, thereby "making a famine where abundance lies." In fact, the sonnet as a whole can be encapsulated under the theme of the ravages of time, as a one-line summary of its content might be made thus: "Have a child now, beautiful man, because the clock is ticking; don't be selfish."
In line 11, the word "content" could have two very different meanings depending on the position of the stress. If we follow the iambic rhythm, the stress falls on the second syllable, giving the word the meaning of "happiness" or "pleasure," i.e. "you are burying your happiness within yourself." However, some scholars have suggested that the poet is actually making a pun, with the alternate meaning of "content" (stress on the first syllable) a reference to the fair lord's content, his beauty (or even semen: the fair lord is keeping it all to himself, thereby wasting it). It is clear that the poet was very deliberate in his choice of words - his sonnets and plays show numerous other examples of similarly subtle and bawdy puns - so such speculation may seem more reasonable as one becomes more familiar with the sonnets and Shakespeare's work as a whole.