A metaphysical conceit is a drawn out metaphor popular among poets from the 17th century. It likens the qualities of people to physical objects and tends to focus on ideas like love and death. Sonnets are a popular form of metaphysical conceit.
Conceit refers to a literary device that plays on a long running metaphor within a written work. Conceits are common in poems, short stories and novels and are a well known device used in Shakespearean plays. These tools convey humor, express love or mourn mortality.
Metaphysical conceit is associated specifically with the poets and works of 17th century metaphysical writers. Compositions from that period are heavily laden with conceit and are often completely comprised of it as a single literary device. This writing style leads to very convoluted explanations of various emotional states and physical circumstances, likening people to everything from cartography tools and insects to celestial bodies and surgical procedures.
The practice of creating conceits in literature is long standing, but the difference between a conceit and a simile or metaphor is the extreme difference between the subject at hand and the thing to which it is being compared. The less a juxtaposition makes sense in a poem or story, the more likely it is to be a metaphysical conceit.