There are so many important symbols in A Thousand Splendid Suns and, because you asked for two, I thought it might be interesting to speak of an obvious one and one that isn't so obvious: the burqua and snow.
The first (and more apparent) symbol is the symbol of the burqua. A burqua, of course, is an all-encompassing blue or black covering that a Muslim woman wears. The dictionary definition is as follows:
A loose, usually black or light blue outer garment worn by Muslim women that covers the head and face and sometimes the entire body.
The burqua in A Thousand Splendid Suns is a symbol of being trapped under the rule of man. "Luckily," through this trap, the women also are able to hide their negative emotions about their state in life. What is also interesting is that, although women are not required to wear a burqua at home with their family, the husband do require them to wear one when they go out into public. Therefore, the women are not able to hide their emotions to their husbands, only to other men. As a result, they are truly trapped.
A second (and less apparent) symbol in A Thousand Splendid Suns is the symbol of snow. It is Mariam who watches from her window as the snow falls down. She is trapped under the influence of her abusive husband, Rasheed. Mariam thinks about the words of her Nana saying that each snowflake in a sigh from an individual woman upset by something in the world. They fall upon others and make no noise:
As a reminder of how women like us suffer. ... How quietly we endure all that falls upon us.
So, even though it is a lesser known symbol in the book, snow is an IMPORTANT symbol. The women of A Thousand Splendid Suns are ever oppressed and must vent their emotions in some way in order to keep on living.