What's he saying?
"Is it for fear to wet a widow's eye, / That thou consum'st thy self in single life?"
Do you remain single because you're afraid of leaving behind a mourning widow?
"Ah! if thou issueless shalt hap to die, / The world will wail thee like a makeless wife;"
If you happen to die childless, the whole world will miss you;
"The world will be thy widow and still weep / That thou no form of thee hast left behind,"
The world will miss you because you haven't borne a child that looks like you,
"When every private widow well may keep / By children's eyes, her husband's shape in mind:"
While widows can remember what their husband looked like by seeing a resemblance to him in their children:
"Look what an unthrift in the world doth spend / Shifts but his place, for still the world enjoys it;"
Everything that a wasteful person spends in the world shifts from pocket to pocket, so it is continually enjoyed by the whole world;
"But beauty's waste hath in the world an end, / And kept unused the user so destroys it."
But if you don't have children, you destroy your beauty when you die.
"No love toward others in that bosom sits / That on himself such murd'rous shame commits."
So it's selfish and unkind toward the whole world to not have a child.
Why is he saying it?
Sonnet 9 is one of the "procreation sonnets," Sonnets 1-17. In these sonnets, the speaker tries to convince the fair lord, to whom the first 126 sonnets are addressed, to have children. Sonnet 9 takes the approach of suggesting a reason the fair lord might be reluctant to have children in the first line: "for fear to wet a widow's eye," or to leave behind a mourning widow when the fair lord inevitably dies. But the speaker points out over the course of the sonnet that this is a silly idea, since if he does not marry and leave children to replace his beauty, he will be, in effect, widowing the whole world.
The fate of an ordinary, "private" widow is discussed in lines 7-8: ""When every private widow well may keep / By children's eyes, her husband's shape in mind." The eyes here represent the entire person; the "children's eyes" are the children themselves. So by looking at her children, the widow is able to remember what her husband looked like when he was young and in his prime. In Sonnet 5, the fair lord's "gaze" was similarly used to describe his whole person.
In order to interpret lines 9-10, it must be noted that in the Elizabethan era, "its" was not used as a possessive pronoun. So in line 10, "his" refers to the money that is moving around from pocket to pocket. "Look what" means "whatever," or "everything," and an "unthrift" is a prodigal person, or someone who spends money unwisely. When a spendthrift spends money unwisely, it circulates among the people of the world even after his death.
In contrast, a spendthrift with "beauty" does not leave such a mark on the world after death. Lines 11-12 create a contrast between the spendthrift and the person who does not procreate, pointing out that "beauty's waste hath in the world an end." As in Sonnet 6, these lines contain a warning against masturbation, thought to be a waste of semen. In the seemingly contradictory line 12, the "user" is the fair lord, and the "unused" beauty is the semen that is not used to impregnate a woman.
The couplet that ends Sonnet 9 seems a bit intense as a scolding of the fair lord for not procreating, accusing him of committing "murd'rous shame" on himself. But this phrase can be seen as an extension of the masturbation innuendo; in wasting semen, it is as if he is murdering potential children. The speaker tells the young man that clearly he has "no love toward others" in his heart, if he acts so selfishly as to not bear children in his image for the world to enjoy. This accusation of selfishness is also apparent in Sonnets 1 and 3.