In the previous mitzvah, we discussed how one may take whatever steps necessary to save an innocent person from a pursuer who intends to kill him, up to and including killing the pursuer, if necessary. In this mitzvah we see that doing so is not optional. We must kill the pursuer if doing so will save the victim.
As to the reason underlying this mitzvah, the Sefer HaChinuch merely refers us to that of the preceding mitzvah, presumably that the one being pursued calls out to God, so God obligates us to help him. If I might be permitted to share my own thoughts on the matter, it would seem that some people might be too squeamish to kill someone, even in defense of the innocent. They might figure, "No matter what, someone is going to die in this scenario, so let it not be at my hands." This mitzvah informs us that the situation is not a zero-sum game. One person is innocent and the other is guilty. If someone has to die, let it be the guilty person. In such a case, the one who carries out the unpleasant duty is not only blameless but meritorious.
This mitzvah applies in all times and places. It is discussed in the Talmud in tractate Sanhedrin on page 72b and in the Mishna in the seventh chapter of tractate Ohalos. It is codified in the Mishneh Torah in the first chapter of Hilchos Rotzeiach. This mitzvah is #293 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos; it is not listed in the Chofetz Chaim’s Sefer HaMitzvos HaKatzar.