It says in Masechet Sofrim (chapter 14; listen to audio for precise citation) that when the Torah is taken from the Heichal for the Torah reading, it should be lifted and shown to everybody in the synagogue. Upon seeing the writing of the Torah, everyone should bow and recite the verse, "Ve'zot Ha'Torah Asher Sam Moshe…" (Devarim 4:44). The Talmud Yerushalmi (Sota 7:4) derives this Halacha from a verse in the Book of Devarim (27:26), "Cursed is the man who does not uphold the words of this Torah," which can be understood as reference to one who does not lift the Torah scroll to show it to the congregation. This Halacha is indeed codified in the Shulchan Aruch, (O"H 134:2).
The Arizal (renowned Kabbalist, Israel, 1534-1572) commented that sparks of sanctity emerge from the Torah scroll when it is taken from Heichal for the Torah reading, and it is therefore a Mitzva to look upon the actual writing of the Torah (Magen Avraham, S"K 3). The one who removes the Torah should lift and bring the Torah around the entire synagogue so that everyone, both men and women, can see the writing. Rabbi Avraham Palachi (Turkey-Israel, 19th century) records a custom to look in the Torah for a word that begins with the same letter as one's name. For example, a person named "Avraham" would look to find a word that begins with the letter "Alef." (See Ben Ish Hai, Shana 2, Parashat Toledot, Ot 16.)
When the Torah scroll is returned to the Heichal after the reading, should it be carried to the Heichal opened or closed?
The Ben Ish Chai (Rabbi Yosef Chayim of Baghdad, 1833-1909) held that the sparks of sanctity do not shine forth from the Torah after it is read, because the Mitzva had already been completed, and therefore it should be kept closed as it is returned to the ark. By contrast, Chacham Ovadia Hadaya (Israel, 1890-1969), in his work Yaskil Avdi, Helek 8, Siman 24, held that the Torah scroll leaves some impression even after the reading, and therefore it should be carried to the Heichal opened.
Different customs exist in this regard, and Chacham Ovadia Yosef, in his work Yabia Omer, Helek 7, O"H Siman 16 (in the margin), rules that each community should follow its custom, as both are firmly rooted in Halacha. Our community follows the practice of keeping the Torah closed while it is returned to the ark, but if there were people in the synagogue who did not see the Torah when it was taken from the Heichal, it would be permissible to open the Torah while it is returned to give them this opportunity.
Summary: When the Torah scroll is removed from the Heichal, it should be opened, lifted and carried around so that everyone in the synagogue can see the script. Some communities have the practice of keeping the Torah opened when it is returned to the Heichal, as well, while others keep it closed, and each community should follow its custom.
