The halachic commentators suggest two reasons for this rule. Firstly, in order that one praying should not have his or her concentration disturbed. Secondly, because the Divine Presence is in front of a person saying the amidah. According to the first explanation, if a person is praying with his eyes closed, and as consequence cannot be disturbed, this prohibition is not applicable. However, according to the second explanation, it is not relevant whether or not a person praying will be disturbed.
Most halachic authorities advise a stringent approach in accordance with the second opinion.
Whilst it is permitted to pass at the side of a person praying, there is a dispute amongst halachic decisors regarding the sideways area in front of such a person. Though some prominent authorities consider this area as being in front and therefore out of bounds, the Aruch Hashulchan and other codifiers have ruled leniently in this regard. Because of this rule, when one takes three steps backwards at the conclusion of the amidah, it is important to establish that the person standing directly behind has also finished praying. Interestingly, the Aruch Hashulchan rules that the Rabbi of a community need not be concerned about this detail. In a similar vein, a contemporary rabbinic authority has ruled that a Kohen who is on his way to duchan may also pass in front of someone still reciting the amidah.