Aside from symbolism, George RR Martin also uses parallelism of events, of characters and symbolism. Especially in the writing of an epic story of an alternative universe or world with its own history going back thousands of years that involves thousand characters or so, paralleling past with the present, or across continents can be a very useful tool.
George uses point of views to tell his epic story. But they may be biased or at an age that limits their understanding of a situation. By paralleling a similar, but different situation for another point of view character George can provide a commentary on the initial event and the characters involved in that situation. Take for example the captive situation of Arya, Gendry and Hot Pie (2 boys and 1 girl) at Harrenhal in aCoK. In aDwD Tyrion, Jorah and Penny (2 men and 1 woman) also end up in a captive situation, and George parallels those two different events heavily, including the impact it has on the different characters involved. Tyrion though is much older than Arya and able to theorize and comment on what slavery and forced labor can do to a person. Reading Tyrion’s commentary on the parallelled situation sheds a different light on Gendry’s reluctance to escape. It helps us realize that Gendry talks like a slave who praises his slave master, out of gratitude for his captor’s kindness and relative safety in comparison to others; and that the bravery he displays on the King’s Road and the holdfast attacked by Ser Amory is broken in the same way that Jorah is broken.
Parallelism can be used to reveal something of a past event that predates the events in the books and we only know of through hearsay as well as foreshadowing of future events. I showed in Chthonic Cycle – The Cursed Souls of Eddard and Robert how the chapter that ends with the street brawl between Jaime Lannister and Ned Stark in King’s Landing parallels with the dream of the Tower of Joy, and how that parallel gives us clues about the past, in case you were unaware of the R+L=J theory. Lucifer Means Lightbringer shows how the myths of Azor Ahai, and the origin of dragons and the second moon are paralleled repetitively over time and in different plot arcs. And the parellelism of fire and blood and swords and dragons tells us both something of the past as well as the possible upcoming plot for the next books.
Finally, parallelism can be used as a tool to teach the reader symbolism. When we compare the symbolism of the crypts of Winterfell with that of the dungeon Eddard Stark land in, we can infer that the later is a symbolic parallel location, where Ned Stark turns into a statue as blind and immobile as the Kings of Winter in the crypts. But Ned is still alive and there is no iron sword in his lap to prevent his spirit to curse those who betrayed him.
It is thus a very valuable tool for both the author as well as the reader to gain deeper understanding of the story. Much of the parallelism can be discussed within its certain mythical sphere. But some fall outside of it and stand symbolically on their own. You will find essays and predictions based on such parallels in this section.