We're not so sure that A Game of Thrones has symbols in the way that we usually think of symbols in books. It's not like "rivers are connected to the theme of longing," or anything like that. Rather, we think that our reading process is helped along by a few recurring images or issues, like the noble family's symbols and mottoes. Does a family symbol really symbolize something? We're not so sure. But the system of family symbols does communicate information to us and so it makes our reading easier. And since we're jumping into this totally imaginary world, having a little help like this is much appreciated.
So, the house sigils. Don't be thrown by the word "sigil" – it just means sign or symbol. In this case, it refers to the noble houses' particular symbols.
The most obvious symbol in this book is the system of heraldry (which is definitely connected to the importance of family). For instance, the Stark family symbol is the gray direwolf on white; the Baratheon symbol is a male deer (a stag) with a crown, black on gold; and the Lannister symbol is a golden lion on a red field. (These symbols are so important that Martin lists all of them in the Appendix at the back of the book.)
Every house has their own symbol, and Bran can tell who is coming to Winterfell by which banner they wave:
The maester had taught him all the banners: the mailed fist of the Glovers, silver on scarlet; Lady Mormont's black bear; the hideous flayed man that went before Roose Bolton of the Dreadfort; a bull moose for the Hornwoods; a battle-axe for the Cerwyns; three sentinel trees for the Tallharts; and the fearsome sigil of House Umber, a roaring giant in shattered chains. (54 Bran 6.7)
For more examples of house symbols telling us who is where, see the description of the participants in the Hand's tournament, where their house symbols are painted on people's shields (31 Eddard 7.9); or Tyrion's description of the battle, where "The white of House Stark was seen everywhere, the grey direwolves seeming to run and leap as the banners swirled and streamed from the high staffs" (63 Tyrion 8.106). Awesome imagery.
(If you're not a big medieval nerd like us, you might think that Martin is inventing this, but he's really not. Heraldry was – and still is – a big deal because it could tell you several things about the noble families and those families that desperately want to be noble. Read more about it here.)
Okay, now we have the background. Sure these symbols are useful to the characters in the book, but they are also useful for us. Let's take a look.
(1) Some of these house symbols tell us about the houses and characters. For instance, Roose Bolton's symbol is like something out of SAW – a man without his skin – and that tells us something about the Boltons: they're dangerous. And a little scary. (And also go through too many sequels. No, wait, that doesn't sound right.)
(2) House symbols may also be modified by individuals, and that may tell us something about those individuals and their relationship to their house. For instance, the Tully family symbol is a leaping silver fish; but Brynden Tully is sort of the black sheep of the family, so he takes a black fish as his person symbol. (He can do that since he's not the main lord of his house. His brother Hoster is in charge of the Tully lands, so he couldn't really change the house symbol all that much. But since Brynden is only responsible for his shield, he can pretty much paint whatever he wants there.)
(3) Get this: this system of house symbols leads us to looking for symbols elsewhere in the book. Yeah, that's right. The prime example of this is probably real early on in the book, when the Starks find a dead direwolf, killed by a stag horn. Jory Cassel thinks this is a sign (2 Bran 1.48); and since we know what house has what symbol, it seems like this is a sign saying that the Baratheons (the stag) are going to kill the adult Stark (the adult direwolf). What do you think? Does it match up?
Are there other examples of these house symbols giving us information about this world?
When we look at the symbols of the noble houses, we should also look at the house mottoes. Let's start with an example. Catelyn says to herself:
"Every noble house had its words. Family mottoes, touchstones, prayers of sorts, they boasted of honor and glory, promised loyalty and truth, swore faith and courage. All but the Starks. Winter is coming, said the Stark words. Not for the first time, she reflected on what a strange people these northerners were." (3 Catelyn 1.15)
So the Stark motto not only reminds us that there's a bigger fight out there than just the civil war; it also tells us something about this family's philosophy, which definitely affects the characters. (Notice how Catelyn thinks about things differently than Eddard; part of that is probably that they grew up in different families, taking different mottoes as their guides. Pretty neat, right?)
And, as Catelyn notes, the Stark words are so different from the other houses' mottoes, which reminds us that the north is almost like a different country from the Seven Kingdoms. Basically, these mottoes represent, quite literally, the attitudes of each house.
(For other fun uses of mottoes, note that Petyr Baelish uses the Tully words – "Family, Duty, Honor" – to indicate that he knows when Catelyn is lying [19 Catelyn 4.69]; and Tyrion uses the Arryn words – "As High as Honor" – to make sure that he gets a fair trial [41 Catelyn 7.92]. Why does Catelyn keep getting tripped up by these mottoes?)