There are several instances in "To William Shakespeare" where Jonson describes the deceased poet as somehow being raised, above, or higher than other people and things. This is fairly common in elegies, as heaven is generally thought of as being "up," but Jonson isn't talking about Shakespeare's afterlife in the religious sense. Here, the elevation imagery is used to symbolize Shakespeare's elevated status as compared to his literary peers and also the way in which he elevated the quality of the theater during his lifetime.
Line 12: We're first introduced to the concept of elevation in line 12, when Jonson clarifies that he is not writing a tongue-in-cheek kind of poem that sounds flattering but actually isn't. His goal is to "raise" Shakespeare, but there's a pun here, too. The word raze, which sounds the same even though it's spelled differently, means to destroy or flatten.
Line 15: Shakespeare is described as being "above" the criticism and ill fortune that occasionally befalls writers. This establishes a theme that will be continued through the rest of the poem, so keep your eyes and ears peeled for more.
Line 19: Jonson commands Shakespeare to "rise" in a drama-ridden tone appropriate for commanding someone to come back from the dead. Here, "rise" refers not only to Shakespeare's resurrection in the form of the First Folio but also his superiority to the other British authors named in the stanza.
Line 71: Jonson directly compares Shakespeare to a swan, flying gracefully along the banks of the Thames. Swans are a pretty loaded image, symbolically speaking, but we're going to unpack a couple of the potential angles Jonson might have been getting at here: (1) The Mute Swan of Europe is, as you might have guessed, a swan that is native to Europe that does not make any noise. Popular culture, however, theorized that the Mute Swan, upon dying, would sing beautifully for the first and only time in its life. This is where the phrase "swan song" comes from, but also a cool potential parallel for the now-dead Shakespeare and his swan song, the First Folio. (2) In classical mythology, which we know Jonson loves, the most famous swan comes from the story of Leda and the Swan (warning: this story ends with Zeus, disguised as a bird, raping the Queen of Sparta). Here, though, we think the swan's association with Apollo (a Greek god with whom Jonson has already compared Shakespeare) is more appropriate. Swans were basically the bird mascot of Apollo and are often depicted as pulling his chariot. (3) Swan was considered a luxury food item back in the days of Queen Elizabeth. You can find a recipe for baked swan here. Note: Shmoop doesn't actually think this is relative to the poem, but it's good information to have on hand in case you ever find yourself needing to make an early modern English feast.
Lines 75-76: Jonson gives Shakespeare the ultimate elevation boost and turns him into a star. This is a gesture that was often used by the classical poets, who thought that the stars were immortal.
Line 88: What goes up must come down, and Jonson seems to know this was the fate of the theater as well. His description of the stage as "drooping" after Shakespeare's death may just be a symbolic one, but Jonson was spot on: the next few years would see a rapid decline in the quality and output of the theater, ultimately culminating in it being temporarily outlawed by some rather entertainment-unfriendly Puritans.