One medieval idea that carries over into Renaissance art and literature is the Great Chain of Being, the notion that every living thing has a specific rank in the divine scheme of things. Think of it as an early take on the class system. Donne makes references to people and things all up and down the chain of being: schoolboys, apprentices, hunters, royalty, farmers, even ants. He is arguing that the whole scope of humanity is subject to the sun's power, but (you guessed it) he and his lover are exempt. Their love breaks free of that chain.
Lines 5-8: This is a fairly classic Donne list of different classes of people. The next lines then claim that love (namely, his love) transcends all of them.