Our Gemara on Amud Aleph discusses two proof texts for the requirement to be silent when the Torah is being read.
אָמַר רָבָא בַּר רַב הוּנָא כֵּיוָן שֶׁנִּפְתַּח סֵפֶר תּוֹרָה אָסוּר לְסַפֵּר אֲפִילּוּ בִּדְבַר הֲלָכָה שֶׁנֶּאֱמַר וּבְפִתְחוֹ עָמְדוּ כׇּל הָעָם וְאֵין עֲמִידָה אֶלָּא שְׁתִיקָה שֶׁנֶּאֱמַר וְהוֹחַלְתִּי כִּי לֹא יְדַבֵּרוּ כִּי עָמְדוּ לֹא עָנוּ עוֹד רַבִּי זֵירָא אָמַר רַב חִסְדָּא מֵהָכָא וְאׇזְנֵי כׇל הָעָם אֶל סֵפֶר הַתּוֹרָה
Rava bar Rav Huna says: Once a Torah scroll has been opened, it is prohibited to converse, even about a matter of halakha. As it is stated: “And Ezra opened the book in the sight of all the people, for he was above all the people, and when he opened it, all the people stood up” (Nehemiah 8:5), and standing is referring to nothing other than silence, as it is stated: “And shall I wait, because they do not speak, because they stand still, and answer no more?” (Job 32:16). Rabbi Zeira said that Rav Ḥisda said: The prohibition against conversing is derived from here: “And the ears of all the people were attentive to the book of the law” (Nehemiah 8:3). They were not listening to any other voice.
It is notable that the first proof comes from a language of standing still, at attention, while the second proof comes from a language of intently listening. The distinction between standing at attention and listening intently may be represented in various halakhic disputes regarding this directive.
Tosafos on our Gemara notes a contradiction between this statement and what is recorded about Rav Sheshes in Berachos (8a), that he turned his head away during the Torah reading and did his own study:
רַב שֵׁשֶׁת מַהְדַּר אַפֵּיהּ וְגָרֵיס. אָמַר: אֲנַן בְּדִידַן וְאִינְהוּ בְּדִידְהוּ.
The Gemara relates that Rav Sheshet would turn his face away from the Torah while it was being read and study. Explaining this practice, he said: We are engaged in ours, the study of the Oral Torah and they are engaged in theirs, listening to the Written Torah. Since Rav Sheshet was engaged in Torah study, he is not considered one who forsakes the Lord.
Because of this contradiction, Tosafos offers several suggestions as to what is the difference between Rav Sheshes’ situation and our Gemara. Many of the distinctions given by Tosafos are codified in Shulkhan Arukh (OC 146:2)
כיון שהתחיל הקורא לקרות בספ' תורה אסור לספר אפי' בד"ת אפי' בין גברא לגברא ואפי' אם השלי' הוא הפרשה ויש מתירים לגרוס [פירוש ללמוד] בלחש ויש אומרים שאם יש עשרה דצייתי (פירוש שמשימין לבם) לספ' תורה מות' לספ' [בדברי תורה] (ב"י בשם מהרי"א) ויש מתירין למי שתורתו אומנתו ויש מתירין למי שקוד' שנפתח ס"ת מחזיר פניו ומראה עצמו שאינו רוצה לשמוע ס"ת אלא לקרות ומתחיל לקרות ולקרות שנים מקרא ואחד תרגום בשעת קריאת התורה שרי וכל זה אינו ענין לפרש' זכור ופרשת פרה שהם בעשר' מדאוריית' שצריך לכוין ולשמעם מפי הקורא והנכון שבכל הפרשיות ראוי למדקדק בדבריו לכוין דעתו ולשמעם מפי הקורא:
Once the reader began reading from the Torah, it is forbidden to speak even words of Torah, and even between one aliyah and the next, and even if one already finished the parsha. And there are some who permit learning quietly. And there are some who say that if there are ten men who are listening (meaning, they are paying attention) to the Torah reading, then it is permitted to discuss [words of Torah] (Beit Yosef in the name of Mahari"a). And there are some who permit it for those for whom Torah is their profession. And some permit it for one who turns his face away before they open the Torah scroll, who [by doing so] indicates that he does not wish to listen to the Torah reading, but rather [wants] to learn, and he may begin learning. And to recite "Shnayim Mikrah, Ve'echad Targum" (ie. the practice of "reading [each verse] twice, and [the aramaic] translation once") during the Torah reading is permitted. And all this is not regarding Parshat Zachor and Parshat Parah which must be read with [a quorum of] ten [men] due to them being Torah level mitzvot that one must concentrate and hear from the reader. And it is proper that for all the parshiot [throughout the year], it is fitting to be scrupulous with these things and pay attention and hear them from the reader.
Mishna Berura (ibid 4) notes there is a dispute amongst the poskim if the prohibition begins from the moment the Torah is open or from the moment of reading. It is possible that the two different proof texts speak to each side of the coin. That is, the second proof text has an emphasis on listening. Perhaps that is only the obligation to be silent once the reading has begun. However, the first proof text emphasizes standing still at attention. That implies a preparatory meditative state required, and may begin even before the reading.
Similarly, there is a discussion amongst the poskim (ibid 6) as to whether the prohibition applies between Aliyos. Once again, we can say that this question depends on the two verses. If the requirement is merely to listen, we might argue that it is not necessary to refrain from talking between the Aliyos. However, if the requirement is to be in a meditative, focused state, the requirement might extend throughout the entire period of the reading, including between the aliyos. (Although some poskim prohibit talking between the Aliyos merely as a matter of practical concern that most conversations will end up leaking over into the regular reading. Yet some even prohibit quiet Torah study between the Aliyos, and therefore, must be informed by an additional requirement.)
There is also a disagreement amongst poskim if there is duty to stand during the reading (Mishna Berura ibid 19). Technically, our Gemara does not use the word “stand” in the proof text of the people during the time of Ezra, as literally standing, and instead, it was understood as focused, still and at attention. Yet, Shu”t Binyamin Zev (163) argues that one never removes the verse from its plain straightforward meaning. Therefore, we must understand that there also is an obligation to literally stand during the reading.
Regardless, we can see that there are quite possibly two different modes of paying respect to the Torah reading. One requirement is to listen and pay attention to the words. The other requirement might be to also enter into a thoughtful, reflective state of mind. Along these lines, we find Likkutei Torah (Nasso 1:15-20) drawing a comparison between the pillars in the Mishkan which were also described at standing, and the person in service of God. As in our Gemara’s exegesis, standing is not merely standing; it is being in a contemplative, quiet state. Likkutei Halachos says this means a state of knowing one’s own personal ego and bias, letting all of that go, and becoming completely attached to the will of God. This is comparable to the wood pillars in the Mishkan as the word in Hebrew for wood “Eitz” also means, essential bare-bones (eitz=etzem). The pillars represented a single, focused, intention, to hold up the Mishkan, i.e. the will of God. So, too, the contemplative state of standing and meditating during the reading of the Torah is not just about listening, it is about absorbing the message and letting God’s will and Ethos become yours.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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