In addition to the answer above, which admirably explains the meaning of the lines, I would like to put these lines in a larger context. As you are undoubtedly aware, John Dryden's great mock-epic satire Mac Flecknoe: or, a Satire upon the True-Blew-Protestant Poet, T. S. (written in 1678, published in 1682) was written to counter several attacks on Dryden's poetic and dramatic skills, as well as his politics, by Thomas Shadwell, a playwright who also happened to be Dryden's political opposite. Several of Shadwell's attacks were personally abusive, and Dryden's ultimate response to Shadwell, whom Dryden believed was not only his social inferior but a writer without true talent, was Mac Flecknoe.
Because the poem is a mock-epic, its language and subject must be lofty and mimic the conventions of epic poetry, but its subject is essentially trivial. The loftier the diction and treatment of the subject--in this case, Shadwell--the greater the satiric effect. The two lines you quoted above are meant to establish the tone of an epic with a seemingly profound statement about the brevity of human life, but these lines only serve to set up the framework of Dryden's satire:
All humane things are subject to decay,
And, when Fate summons, Monarchs must obey:
This Fleckno found, who, like Augustus, young
Was call'd to Empire, and had govern'd long. . . . (ll. 1-4)
Richard Flecknoe was a poet and writer of travel literature, but his verses, which are not terrible, evoked some laughter among other poets, such as Andrew Marvell, and later, Dryden, when he used Flecknoe in his mock-epic as the poetic father of Thomas Shadwell. The opening four lines describe the death of Flecknoe and compare him to one of the greatest Roman emperors, Augustus, a clear sign that what follows will not be flattering to Shadwell, who is described a few lines later as
who most resembles me:
Sh-- alone my perfect image bears,
Mature in dullness from his tender years. (ll. 15-16)
The title Mac Flecknoe is meant as a kind of parody on the Gaelic naming convention for a son--Mac--and so the title is The Son of Flecknoe, and Shadwell is the heir of a writer of bad (in Dryden's view) verse.
The opening lines of the poem, then, are meant to establish the tone of an epic, and that is their only purpose. The meaning of the lines, of course, can be taken as profound, but that is Dryden's way of setting Shadwell up for a poetic fall.