Based on the Gemara (Berachot 31b), the Shulhan Aruch (O.H. 102:1-4) rules that one may not sit or pass by within four Amot (roughly 6 feet) of one who is reciting the Amida. Regarding passing by, the Elya Rabba writes that it is not permitted because such an act will distract the one who is reciting the Amida. The Haye Adam, however, says that the reason is that the Shechina-Hashem’s Presence-surrounds the one praying the Amida and walking by the Shechina would be improper. The practical difference between these two opinions involves a Halachically-valid Mehitza. A Mehitza is a partition which has implications for Shabbat, a Sukkah, etc., and measures ten Tefahim high and four Tefahim wide. (It should be noted that in the context of this Halacha, Mehitza does not refer to a partition that is used to separate men and women during prayer.) This Mehitza can be anything from a chair, to a table or the like. According to the Haye Adam, such a Mehitza will be effective to create a partition between the one praying and the Shechina, and therefore one would be able to walk by even within four Amot. According to the Eya Rabba, on the other hand, a Halachic Mehitza is not effective in preventing a passerby within four Amot from distracting the one praying and thus one would not be able to walk by. Only some sort of partition that is taller than the one praying would be satisfy both opinions. Rabbi Yaakov Hagiz (originary of Fes, who later became well known in Jerusalem in the 1600’s) in his monumental work Hilchot Ketanot, (vol. I, § 4), concurs with the Elya Rabba and says that a Halachically-valid partition is not sufficient to prevent a passerby within four Amot from distracting one who is praying.
Another practical application is in a circumstance when one prays at the entrance way of a synagogue. On one hand, one is not permitted to pass by one who is in the middle of the Amida, but on the other hand, if one cannot pass, one will not be able to enter the synagogue until the person praying finishes. Rabbi Avraham Buchach (Eshel Avraham) and Rabbi Shalom Schwadron (Da’at Torah) write that a person does not have the permission to render a public passageway off-limits to other congregants by standing there for the Amida. As such, they and others, such as Rabbi Eliezer Waldenburg (Tzitz Eliezer, vol. IX, § 8) write that in such a case, it is permissible to walk within four Amot by someone who is praying so that one can get into or around the synagogue.
Although there are circumstances when one may be lenient regarding where one prays or where whom one passes by, in general one should be careful to to afford others the proper room to pray.
Summary: One may not sit or walk within four Amot by one who is reciting the Amida