We blow shofar one hundred times on Rosh Hashanah. This is a minhag that is now almost universally practiced. The Gemara does not mention it. Tosafos (Rosh Hashanah 33b) and other sources quote the minhag to blow one hundred times as corresponding to the cries of em Sisrah, Sisrah’s mother. Sisrah was a rasha and was fighting in the war against Devorah and Barak. The Navi (Shoftim 5) describes that em Sisrah was crying because Sisrah was late coming home.

Why was he late? We know that Yael had killed Sisrah. Sisrah is dead and em Sisrah is crying. The mesorah is that she cried one hundred times. Therefore, we blow shofar one hundred times to correspond to her one hundred cries. One source says that if you count up the letters of the pesukim that describe em Sisrah crying there are one hundred letters, so that is the remez to one hundred cries.

Why did a minhag develop corresponding to em Sisrah? She was a marsha’as and her son was a rasha. Why should we have a minhag of one hundred sounds of the shofar corresponding to em Sisrah’s one hundred cries? This is a famous question.[i]

One standard p’shat is mentioned in The Book of Our Heritage, where R’ Kitov zt”l writes as follows. When em Sisrah was crying, her friends were trying to comfort her and said- maybe Sisrah is late because he is killing people, maybe Sisrah is late because he is pillaging the cities. The excuses had a barbaric message. What a barbaric thing to say! “It is okay, don't be upset, maybe your son is late because he is murdering people.” The Book of Our Heritage says that we blow shofar one hundred times to show the contrast. Em Sisrah cried one hundred barbaric cries, but we cry, through the sound of the shofar, for positive things.[ii]

R’ Soloveitchik zt”l said another p’shat.[iii] Em Sisrah was crying, and her friends were comforting her, but she was still crying. Why? Because she knew the truth. Deep down, she knew the emes. What was the emes? Her son was dead. Therefore, em Sisrah’s crying reflected the idea that despite all the excuses her friends were giving her, deep down she knew the emes. It was all a smoke screen. The excuses were not emes; the emes is that her son was dead, so she cried. That, the Rav explains, is what tekias shofar is all about. A person may be involved in an aveirah, and he makes excuses for himself- my friends do the same thing, this is just who I am, it is impossible to change, etc… People make excuses for the aveiros they are involved in. But, deep down we know what the emes is. These are not good excuses. When we blow the shofar, it pierces our hearts and gets to the emes. Wake up! Deep down we know the emes, we want to serve Hashem better. Just like em Sisrah knew the emes deep down and kept on crying despite all the excuses, every Jew has to wake up and recognize the emes that deep down he should be serving Hashem better. This is a beautiful, powerful p’shat from the Rav.[iv]

[i] The connection to em Sisrah has a basis in the Gemara (Rosh Hashanah 33). The Torah uses the word truah to describe the sound of the shofar. Onkelos translates truah as yebava. When the Navi describes em Sisrah crying, it does not say “va’tivkeh” which is the normal way to say, “to cry.” Rather, it says, “va’teyabev.” The root that the Navi uses to describe em Sisrah crying is the same root that Onkelos uses to define the truah of Rosh Hashanah in the Torah. Therefore, we see that there is some sort of hint in the Navi that em Sisrah's crying might be linked up to tekias shofar. That might be another basis of where the minhag started. 

[ii]  Book of Our Heritage, p.21

The purpose of the sounding of the shofar is to arouse Hashem's compassion for the descendants of Yitzchak, who was offered like a ram on the altar, while the lament of Sisrah's mother was an expression of grief suffused with animosity and hatred…

Therefore, we implore: May the one hundred shofar sounds of compassion and mercy nullify every one of those outcries…

[iii] Rabbi Soloveitchik on the Days of Awe, p.10

Yet, although overtly anticipating her son's track for return, in a deep recess of her heart, Sisrah's mother tragically sensed that this time he was, in fact, never coming home again. Tosafos states that we are obligated to hear a total of one hundred shofar blasts to parallel the hundred cries of Sisrah's mother as she waited in vain at the window.

Why does the story of a Pagan mother, awaiting her barbaric son, form the halachic basis for the required number of shofar sounds that are blown on Rosh Hashanah? Because upon hearing the piercing tones of the shofar, we must experience a similar emotion as we awaken from spiritual complacency. We must witness our own illusions being relentlessly shattered.

[iv] One of the themes of shofar is that it pierces one's heart and wakes one up to recognize the emes that is deep inside. The Rosh Yeshiva shli”ta mentioned another hint to this idea. We always read Parashas Nitzavim before Rosh Hashanah. The standard reason given is that Parashas Nitzavim talks about the mitzvah of teshuvah; we should all do teshuvah before Rosh Hashanah. Rav Binah shli”ta quoted from the Abir Yaakov zt"l that the opening word of Nitzavim is “atem.” And “atem” has the same letters of “emes.” So there is a remez to emes at the beginning of the parshah. This is what teshuvah is about, and this is what Rosh Hashanah is about.  A Jew has to open himself up and find and focus on the emes that is inside.