John Keats wrote this poem in reaction to having read "The Iliad" and/or "The Odyssey" by Homer. In the first 4 lines, the poet says that he has often been to the "realms of gold/...Which bards in fealty to Apollo hold." What he means is that he has read the Greek myths and even has read a different translation of Homer's writings:

Oft of one wide expanse had I been told

That deep-brow'd Homer ruled as his demesne;

But it wasn't until he read Chapman's translation that the story really came alive to him.

Now, to interpret the line you are asking about. By "deep-brow'd Homer," Keats is referring to a sculpted bust of the poet. I've pasted a link to a site where you can see what that bust looks like. Homer is "deep-brow'd," or wrinkled, presumably from deep thoughts. The word "demesne" is an old, archaic term meaning "domain." So Keats is saying that Homer ruled these stories as his domain; they were his territory.