Metaphysical poetry can be a tough read. It is characterized by frequent paradoxes and complicated thought processes. Metaphysical poets often use strange imagery as well. Metaphysics, in a nutshell, deals with a lot of stuff that can't be explained by science, so some common themes within the genre are questions concerning the existence of God, the nature of reality and perception, and consciousness.
Taking those above elements and applying them to "The Dream" allows a reader some insight as to why it is metaphysical poetry. The narrator of the poem constantly flip flops between describing what he/she is seeing and experiencing and what may or may not be a dream.
Also, while the poem doesn't expressly discuss the existence of God, there is frequent religious symbolism in the poem through the repetition of the angel. The angel also allows Donne to use some complex imagery throughout the poem, for example when he references her eyes being similar to lightning or lighting a candle.