In the most common interpretation, the Prince of Peace, who "embraced the gloom" and "walked the night alone", refers to Frodo, who left the Fellowship of the Ring and left for Mordor with only his servant and friend Samwise Gamgee for company. "The Queen of Light" who "took her bow" is taken to refer to Galadriel, a queen of the Elves, signifying that the Third Age is ending and that the Age of Men will begin soon.
Other interpretations of how the lyrics relate to Tolkien exist: one example has the "Prince of Peace" referring to Aragorn. Probably the song's most compelling link to Tolkien is the lyric: "The Ringwraiths ride in black", a Tolkien invention.
However, not everyone agrees that the lyrics of The Battle of Evermore refer to Tolkien's book. An extended commentary in favour of the Tolkien interpretation can be read here: "The Battle of Evermore" and Tolkien