The "realms of gold" in the first line of the poem refers to the translation of Homer by George Chapman that Keats is reading. In this sonnet, Keats compares reading this translation to the discoveries the early explorers made as they circled the globe in search of physical realms (or cities) of gold. Specifically, he compares the thrill of first reading this translation to the awe Cortez and his sailors must have experienced when they first saw the Pacific Ocean. Keats writes that he felt like:

He star'd at the Pacific—and all his men
Look'd at each other with a wild surmise . . .

MUCH have I travell’d in the realms of gold,   
And many goodly states and kingdoms seen;   
Round many western islands have I been   
Which bards in fealty to Apollo hold.

In this, the first quatrain of John Keats’ sonnet, “On First Looking into Chapman’s Homer”, the narrator is discussing the experience of reading poetry. The poem is an extended simile, in a sense almost like one of Homer’s extended similes, that compares reading as a form of imaginative travel, in which the mind journeys although the body does not move, to real journeys or explorations. Keats, as a poor medical student dying of tuberculosis, could not travel across oceans, but he could travel in the “realms of gold”, the world of literature and imagination. The realms of gold in this poem can be considered either those of the imagination in general, poetry, or specifically classical literature. Any of those meanings would apply equally well to his main point.