Metaphysical poetry is characterized by its conceits, extended metaphors that often compare two very unlike things (they are stranger or more unusual than metaphors typically are), and by its argument-like structure. Even though a central conceit may introduce a strange comparison, the poet attempts to use logic to explain or illustrate his ideas. This is definitely the case in John Donne's "The Flea." 

In "The Flea," Donne's speaker tries to persuade a woman to sleep with him before they are married. This would've been riskier for her than for him, since a woman's reputation would be ruined if she had premarital relations. The conceit Donne uses to develop his argument compares a flea to the lovers' potential union. The metaphor, which is extended over the entire poem, compares something romantic (their union) to something decidedly unromantic, and even disgusting (the flea).

At the start of the poem, the speaker tells the woman to look at the flea and imagine that the two of them are joined inside the body of the flea; since the flea has bitten each of them, their bloods mingle in the flea and connect them in a way similar to the romantic union the speaker is pursuing. Donne even goes so far as to suggest that they are married inside of the flea, and that their union has been made sacred in the metaphorical "marriage temple." The speaker uses the conceit to try to convince the woman that the act of sleeping with him will be as minor and blameless as the flea's act of biting both of them and feasting on blood from both of them ("Thou know’st that this cannot be said / A sin, nor shame, nor loss of maidenhead").

The woman later kills the flea, but the speaker is able to turn that to his advantage, as well. The woman "triumph'st" and brags to the speaker that killing the flea did not cause any harm to either of them (the speaker had previously said that killing the flea would be "sacrilege," as she'd be killing the flea and their sacred union at the same time). The speaker ends the poem by saying that in the same way killing the flea did not take her life, sleeping with him will not take her honor. So, in the speaker's mind, his argument has reached its logical conclusion, and since he used an odd conceit to illustrate his argument, "The Flea" is a great example of a metaphysical poem.