Andrew Marvell in his poem "To His Coy Mistress" demonstrates two characteristics of poetry we, today, categorize as metaphysical.
He uses stretched metaphors, for example. In part one of his syllogism, or logical argument designed to convince his target--a woman--to sleep with him, he refers to their love as "vegetable love." The idea is that if they were immortal and could spend centuries in the wooing stage of love making, their love could grow as slowly as a vegetable. The metaphor is stretched, of course. The slow growing rate of a vegetable is not normally compared to love growing.
Secondly, Marvell displays and revels in his wit and intelligence and learning. In the second part of his syllogism, in which he centers on the mortality of humans, he concludes with
The grave's a fine and private place,
But none, I think, do there embrace.
And later, in part three, he says that the lovers should be like "amorous birds of prey."
The grave couplet demonstrates his wit and keeps the poem a little lighter than the morbid imagery might otherwise make it.
The comparison of lovers to loving predators demonstrates both a stretched metaphor and wit.
The stretched metaphors, the wit displayed, and, additionally, the carpe diem theme, mark Marvell as a metaphysical poet.