This is a great question. The significance is twofold. 

First, these are the words that describe Soraya's mother's feelings in regards to her daughter's marriage with Amir. These words might sound rather odd to a Western frame of mind, but within the context of Afghan culture things begin to make sense. Soraya in the past ran off with another man until her father found her and brought her back home. The act of premarital sex and the fact that she had relations with another man before marriage was hugely taboo. She was nearly untouchable. Hence, Amir's decision to marry Soraya was a sigh of relief for Soraya's mother. 

Second, women in Afghan culture were not treated well to a certain extent. There is a chauvamism that lingers. We can see this in the general Taheri's relationship with his wife in a sense. In light of this, for Soraya to have found a great man is another sigh of relief.