Satire is the use of irony, sarcasm, ridicule, or the like, in exposing, denouncing, or deriding vice, folly, etc. (See links below for more information.)
The poem, To His Coy Mistress, is a satire in that it uses sarcasm to point out the fact that time is short, and to argue the point of the narrator that the young lady he is interested in should not deny his advances before time runs out on them. He starts out by exaggerating that if he had all the time in the world, he could take his sweet time and slowly woo her over thousands of years. However, the reality is that the clock is ticking and the narrator realizes that "time's winged chariot [is] hurrying near" and they need to speed up the process before death is knocking at their door. To compel her further, he comically states that, "The grave's a fine and private place, but none I think there do embrace."
In conclusion, the author uses sarcasm to denounce the young woman for being so coy with him, and uses the satire in his poem to politely build his argument for her to embrace him without reserve.