Metaphysical poetry is usually characterized by the poet's attention to a single topic -- usually of a more philosophical nature. The poets that are considered metaphysical all display intellectualism and creativity in their poetry. The poems are clever and witty as well as interesting in how they present the speaker's/poet's stance on a subject.
One of the most famous poems by John Donne is "The Flea." In this poem, the speaker is addressing a young woman and trying to convince her to have sex with him. His argument centers around a flea. At that thought the reader is thinking, "Are you kidding me? The speaker thinks a pesky flea is the stuff of romantic seduction???" But that is exactly what the speaker does (though unsuccessfully.) The poem becomes a clever and witty argument that the flea just bit both of the them and therefore their blood is mixed in the flea and therefore it would be no big deal for their blood to be mixed in the sexual act (Elizabethans thought that kind of thing happened a lot.) The young woman in the poem doesn't accept the argument and she kills the flea, but the reader has to give the speaker credit for trying this, and the poet for the creative take on how to seduce the girl. It is clever, witty, funny, and yet thought provoking at the same time. That is what it takes to be a good metaphysical poem.
Other poems, such as "A Valediction: Forbidding Mourning," are clever in a more serious way. In this poem, he is telling his wife to quietly accept his upcoming departure on business by telling her that their love is greater than everyone else's. He uses metaphors drawn from science, chemistry, astronomy, geometry, as well as clever language to express his love. The most unique metaphor of the poem is his comparison of their relationship to that of a compass like you would use to draw circles. His elaboration of the metaphor creates a conceit. By taking a common object with no prior associations to love and crafting this clever metaphor, Donne proves the qualities of the metaphysical poet here again.