The vessels of the Mishkan (Tabernacle) were carried using poles. Unlike the altar, whose carrying poles were removed when it was not being moved, the poles of the ark had to remain in place at all times.
The reason for this mitzvah is that the ark represented the focal point of holiness in the Tabernacle and, later, the Temple. Containing the luchos, the tablets on which the Ten Commandments had been inscribed by God, the ark was kept in the Holy of Holies, which was only entered by the Kohein Gadol (High Priest) on Yom Kippur. An object of such intense holiness must be treated with the utmost respect and handled as minimally as possible. (Look in 2 Samuel chapter 6, where Uzzah perished after inadvertently handling the ark unnecessarily.)
Also, in the time of the Mishkan, the ark was taken out to battle. If the staves were removed and replaced upon traveling and resting, the possibility existed that some error might be made if the ark needed to be brought out quickly. Perhaps the poles would not be properly replaced because of the rush, leading to the ark being dropped, God forbid. Instead, the ark was kept “ready to go” at all times.
As an aside, the ark is popularly depicted as having the poles running along the longer sides but, according to the Talmud in Menachos 98a-b, the poles actually ran along the shorter ends.
This mitzvah applies to both men and women, in all times and places but it is not able to be practiced today. (The Sefer HaChinuch is quick to point out that this mitzvah is meant to be kept “for all time,” which is why it is included among the 613 mitzvos. The fact that we are incapable of observing it at the present time is irrelevant; it applies at all times.) It is discussed in the Talmud in Yoma 72 and codified in the Mishneh Torah in Hilchos Klei HaMikdash chapter 2.
The prohibition against removing the poles from the ark is #86 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos; it is not includes in the Sefer HaMitzvos HaKatzar because, while theoretically in effect, it is impossible in practice to observe this mitzvah today.