This conversation between Bilbo and Frodo follows after Bilbo recites his own poem about Earendil the Mariner. Poetry played a big role in the history of Middle Earth; it was _created_ through what was described as 'holy music', and The Silmarillion and The Lord of the Rings contain many old poems about historical events. Poetry was held in high regard by the elves, and Aragorn ('he' in your qoute), being a regular guest in Rivendell for hundreds of years, knew this. An attempt by a mere mortal like Bilbo to compose a poem not about Hobbit history, but about one of the defining events of the First Age, surely is out of the ordinary. 'Above my head' is one of the ways to express that in English ('out of my league' would be another idiomatic one).