If an innocent person is being chased by someone with the intent to kill him, we must try to save him, even if it means killing the pursuer. (In Hebrew, the pursuer is called a "rodeif.") The scenario in the Torah involves two men fighting; the wife of one grabs the other by the genitals. The one being grabbed may be saved by any means necessary, up to and including severing the hand. Similarly, in any situation where someone is imperiled, we may do what is necessary to rescue the victim.
One may only kill a pursuer if it's the only way to save the victim. If someone kills a rodeif when he doesn't have to, it's full-fledged murder. (From this mitzvah, the Mishna in Ohalos 7:6 deduces that abortion may be performed to save the mother's life even though it may be impermissible in other situations. The fetus is like a rodeif to the mother and we must do what is necessary to save her.)
The reason underlying this mitzvah is what we have said before about might not making right. The fact that one person has the ability to subjugate another does not give him the right to do so. Since the one being pursued cries out to God for help, God has commanded us to assist him.
This mitzvah applies in all times and places. It is discussed in the Talmud in tractate Sanhedrin on pages 72a-74a. It is codified in the Shulchan Aruch in Choshen Mishpat 425. This mitzvah is #247 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos; it is not listed in the Chofetz Chaim’s Sefer HaMitzvos HaKatzar.