Our Parsha discusses the commandment to construct the Mishkan and the various vessels which would be used in the Mishkan; the first such vessel described is the Aron (שמות כ"ה:י'). Although the Rambam (ספר המצות, מצות עשה כ') and the Sefer HaChinuch (מצוה צ"ה) seem to hold that the Mitzvah to build the Aron is simply a part of the general Mitzvah to build a Mishkan -and subsequently, a Beis HaMikdash- for Hashem to dwell in, the Ramban (בהשגותיו לספהמ"צ, מצות עשה ל"ג) and Rabbeinu Saadyah Gaon ספר המצות( לרס"ג, פרשה נ"ב) disagree, and count building an Aron as an independent Mitzvah. The Ramban (שם) explains that unlike the other vessels of the Mishkan, like the Shulchan, the Menorah, and the Mizbeiach, the Aron was not designed to be used as part of any specific Avodah, but rather to house the Luchos, which represented the presence of Hashem at all times. In his introductory comment to our Parsha, the Ramban writes that the entire purpose of the Mishkan was to contain a place for Hashem's Shechinah to rest; this place was the Aron.
After outlining the particulars as to how the Aron was to be built, the Torah states that its purpose would be to house the "עדות", the testimony which Hashem would give Moshe (שמות כ"ה:ט"ז). The Rashbam (שם בד"ה את העדות) and Ibn Ezra (שם בד"ה ונתת) understand that this refers to the Luchos only, but others, including Rashi (שם בד"ה העדות), believe that this refers also to the entire Torah, and a copy of the Torah was thus also to be stored in the Aron. The Gemara in Bava Basra (דף י"ד.-י"ד:) discusses precisely what was in the Aron. One opinion holds that both the Luchos and a Sefer Torah were kept in the Aron, while the other opinion believes that only the Luchos were there. Both opinions agree that the Shivrei Luchos, the tablets broken by Moshe, were also kept in the Aron, at least eventually, as indicated by Tosafos in Eiruvin (דף ס"ג: בד"ה כל). It is worth noting that even the opinion which holds that a Sefer Torah was not kept in the Aron proper agrees that one was kept on the side of the Aron, in a most dignified and respected location.
The Mishnah in Megillah (דף כ"ח.) implies a comparison between the Beis HaMikdash and our Shuls today, and the Gemara (שם ובעמוד ב') documents the high level of honor and dignity which must be maintained in a Shul. Further on, the Gemara (שם דף כ"ט.), based on a Posuk in Yechezkel (י"א:ט"ז), refers to our Shuls today as miniature versions of the Beis HaMikdash. Some authorities, like the Maharik (שו"ת מהרי"ק שורש קס"א), among others, learn that the sanctity of a Shul is derived from the Torah. The Ran in Megillah (דף ח. בדפי הרי"ף בד"ה ומאן) quotes from the Ramban that the Shul's Kedushah is on a lower level; he himself concludes, however, that the Kedushah is MideRabbanan. In any case, most agree that a Shul has some level of Kedushah, with an accompanying requirement of honor, because of its connection to the Beis HaMikdash; the Shulchan Aruch (אורח חיים סימן קנ"א) documents the type of respect and honor which must be exhibited in a Shul in general.
It thus stands to reason that just as the Aron, where the Torah rested, was the "centerpiece" of the Mishkan and the Beis HaMikdash, as mentioned above, so too should the place where the Torah rests in our Shuls be a place which has special status. The Rambam (פרק י' מהל' ספר תורה הלכה י') indeed implies that a Sefer Torah must be placed in a special location because the Luchos were, and the words which were on the Luchos are contained in a Sefer Torah. The Shulchan Aruch (יורה דעה סימן רפ"ב סעיף א') rules accordingly (עיין שם בביאור הגר"א ס"ק א'). An earlier Mishnah in Megillah (דף כ"ה:) indicates that the תיבה, the "box," where the Sifrei Torah are kept has a higher status of Kedushah than the Shul itself. The Ramo, though (או"ח סימן קנ"ד סעיף א'), writes that this may depend on how this תיבה is built -whether as a separate structure or as part of the wall.
This תיבה, of course, is what we call the Aron, as the Ran explains (מגילה דף ז. בדפי הרי"ף בד"ה בית הכנסת). Actually, it is worth noting that the Gemara in Shabbos (דף ל"ב.) suggests that one must be very careful to refer to the Aron as the Aron HaKodesh, because the word "Aron" alone means simply a box, and it may be disrespectful to use this common word to describe the place where the Sifrei Torah are kept. Tosafos (שם בד"ה על) make it clear that the reference in this Gemara is indeed to the Aron HaKodesh which is in our Shuls. The Maharsha, though (שם בד"ה על), writes that if it is clear that one is referring to the Aron Hakodesh, it is not undignified to call it simply an Aron, as implied by the Gemara in Berachos (דף מ"ז:)
The Rambam (פרק י"א מהל' תפלה הל' ב) rules that the Aron HaKodesh should be placed by the wall of the Shul that the people face when davening so that during davening, they will also face the direction of the Aron; the Shulchan Aruch (או"ח סימן ק"נ סעיף ה') accepts this ruling. In our part of the world where we face east in order to be able to face Yerushalayim, the Aron should thus be on the eastern wall of the Shul. In the Biur Halacha (שם בד"ה שהוא), the Mishnah Berurah questions what direction people should face when davening in a Shul where it was impossible to put the Aron along the eastern wall, whether towards Yerushalayim or towards the Aron, and he leaves it in doubt. Earlier, however, the Mishnah Berurah writes (או"ח סימן צ"ד ס"ק ט') that if the Aron had to be placed somewhere other than on the eastern wall, one should still turn one's face to the east when davening, but never turn his back on the Aron. The Aruch HaShulchan (שם סעיף י"ג) writes that if the Tzibbur is davening in one direction because that's where the Aron is, one should turn just a little bit towards the east so as not to be davening in a direction completely different than everybody else.
Many people have the practice to stand when the Aron is open and the Sifrei Torah are visible. The Taz, however, (יו"ד סימן רמ"ב ס"ק י"ג), rules that this is not necessary strictly speaking, because the Aron is large enough to be considered an independent area, and is thus comparable to the Shulchan, and when the Sefer Torah is on the Shulchan, there is no need to stand. Nevertheless, the Taz writes that people stand anyway when the Aron is open as a sign of respect. For the same reason, the Taz rules elsewhere (שם סימן רפ"ב ס"ק א') that one may stand to give a Drasha with one's back to the Aron HaKodesh, because it is considered an independent domain. But he also writes (או"ח סימן ק"נ ס"ק ב') that one should not position one's seat permanently with his back directly towards the Aron; the Mishnah Berurah (שם ס"ק י"ד) concurs, distinguishing in the Shaar HaTziyun (שם ס"ק י"ג) between a regular and a temporary positioning of oneself with his back towards the Aron.