The beginning of the 4th chapter of Masechet Brachot deals with the reason the Rabbis instituted fixed times for prayer and when the correct time to pray (the Amida) is.
3 fascinating laws are contained in the following piece from today’s daf:
רב איקלע לבי גניבא וצלי של שבת בערב שבת, והוה מצלי רבי ירמיה בר אבא לאחוריה דרב, וסיים רב ולא פסקיה לצלותיה דרבי ירמיה. שמע מינה תלת: שמע מינה מתפלל אדם של שבת בערב שבת, ושמע מינה מתפלל תלמיד אחורי רבו, ושמע מינה אסור לעבור כנגד המתפללין
Rav happened by the house of [the Sage], Geniva, and he prayed [the] Shabbat [prayer] on the eve of Shabbat [before nightfall]. Rabbi Yirmeya bar Abba was praying behind Rav, and Rav finished [his prayer] but did not [take three steps back and] interrupt the prayer of Rabbi Yirmeya. Derive from this [incident] three [halakhot]: Derive from this [that] one may pray the Shabbat [prayer] on the eve of Shabbat [before nightfall]. And derive from this that a student [may] pray behind his Rabbi. And derive from this [that it is] prohibited to pass before those who are praying.
One of these is not normative practice. One is not allowed to daven behind one’s Rabbi. One of the reasons given by the Rabbis is that it will appear that the student is bowing to his Rabbi and this is prohibited.
Whilst it is forbidden to pass in front of someone praying it is permitted to pass by next to them, ideally 4 amot* distance should be kept between the person praying and the person trying to move past them. If in doubt show some patience and don’t disturb those who have not finished davening!
* A short note on biblical measurements:-
The original measures of length were clearly derived from the human body — the finger, hand, arm, span, foot, and pace — but since these measures differ between individuals, they are reduced to a certain standard for general use. The Israelite system thus used divisions of the fingerbreadth(Hebrew: אצבע, Etzba; plural etzba’ot), palm (Hebrew: טפח, Tefah/Tefach; plural Tefahim/Tefachim), span (Hebrew: זרת, Zeret), ell (Hebrew: אמה, Amah, plural Amot), mile (Hebrew: מיל, Mil; plural milin), and parsa (Hebrew: פרסה, Parasa). The latter two are loan words into the Hebrew language, and borrowed measurements – the Latin mile, and Persian Parasang, respectively; the Persian Parasang was approximately (but not exactly) equal to 4 Roman miles.