What is different about this book compared to Hosseini's previous bestseller, Kite Runner, is that A Thousand Splendid Suns focuses far more on the suffering of women in Afghanistan under the Taliban. There are several examples therefore of symbols that explicitly relate to this theme. One of these is introduced by Mariam as she watches the snow fall from her window when she is married to Rasheed and being abused by him. She remembers Nana saying how each snowflake is a result of a sigh that is emitted by a woman who is aggrieved somewhere in the world. According to Nana, all of these sighs go up in to the sky, form huge clouds, then separate once more as each snowflake falls on the people below without any noise:

"As a reminder of how women like us suffer," she said. "How quietly we endure all that falls upon us."

Snow then is an important symbol in this novel because it relates explicitly to one of the central themes: the oppression of women and how, in Afghanistan at the time of the setting of the novel, they had no recourse except for quietly accepting their fate as best as they could.

What are two important symbols and their significance in "A Thousand Splendid Suns"?

The author uses eyes to symbolize the complex emotions of the characters at different times in their lives. After Mariam is taken in by her father Jalil, she discovers that he does not care for her as much as she thought he did. She sees “…the weight of eyes on her” symbolizing the strained relationship between her and her father’s co-wives as well as between her and Jalil. They resented her, looked down upon her and wanted her gone. This realization deeply hurt Mariam. On her bus ride home from seeing the doctor, at the thought of her pregnancy, Mariam’s eyes clearly reflect her emotions. The author says that “It is as though a rainbow melted in her eyes.” The rainbow is symbolic of happiness.

The other symbol in the book is the burqa. This traditional dress whose length reaches the floor and covers one completely from head to toe is symbolic of the hardships of a woman in that society. She has no rights living in a patriarchal society and even her dress code is decided for her. The woman has been denied the opportunity to go to school or work and is subjected to intense hardships to which she has no option but to persevere.

What are two important symbols and their significance in "A Thousand Splendid Suns"?

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.

What significant symbols, besides the burqa, are in A Thousand Splendid Suns?

One other source of symbolism in A Thousand Splendid Suns by Khaled Hosseini is Nana's observation that snowflakes are the falling of "aggrieved" women's sighs that cover people on the earth as a testament of how the world's suffering, undervalued women endure silently. Mariam and Laila are two such women. To clarify, they may talk back as Laila did or even protest as Nana did, but outside of their own four walls, their voices of protest and pleas for mercy are as silent as snowflakes. One other symbol is the reference to Kabul from seventeenth century poetry that says the moons "that shimmer" on Kabul's roofs cannot be counted indicating the glory of Kabul and how the city changes and, then again later, may change again and be rebuilt and restored.