How does the use of second person add to the book's themes?

The Golden Compass is told in third person, not the second person, with omniscient narration. This means the author can move around among characters and places to get inside different characters' heads. Given that Pullman is trying to create the feel of an entire alternate universe, this is an effective method to accomplish this goal. We primarily see events through the eyes of Lyra Belacqua, but the use of third-person omniscient narration allows other perspectives to emerge. For example, we inhabit the point of view of John Faa at the beginning of part 2 and, later, the perspectives of Roger and Lord Asriel.
In part 3, the omniscient narration allows the reader to see events from the perspective of the bears:

Iorek found what he wanted: a firm rock deep anchored in the permafrost.

Later, we learn the following:

The bears knew what they must do.

Although it usually sticks close to Lyra, the ability of the narrative to move into other minds helps this world come alive.