Mesirus nefesh (self-sacrifice, for those who are not so familiar with the term) does not only mean that you were burned at the stake during the Spanish Inquisition. It also means sacrificing your own wishes and desires in order to do what
HaShem asks of you. How do you know what
HaShem wants from you right now? The Rebbeim have instructed us to do what He wants us to do. Determination to carry out the will of
HaShem, without letting anything deter you, that is
mesirus nefesh, which can also be translated as
devoting your soul. This type of
mesirus nefesh is what brought about the miracles of Chanukah.
One of the laws of Chanukah is that you should light the chanukiah (Chanukah Menorah) where passersby can see its light, in order to publicize the miracles that took place during Chanukah. Now, the custom has become to light inside, and not outside the door, as the Gemara says we ought to (there are many explanations as to why we light the candles inside specifically, but we cannot go into them now). This is one of the reasons that the Rebbe instituted the idea of public Menorah lighting -- so that we are able to fulfill the mitzvah of publicizing the miracles of Chanukah in a big way.
Nevertheless, you have to do your part -- in a big way, in a small way, but the world around you has to become brighter and lighter and more Jewish because of you. This is symbolized by the Chanukah candles. In our world today, there are still Jews who don't think only about maintaining their own observance of mitzvos and their own Torah learning. They are aware that there are other Jews around. Not, "I don't care about the rest of the world, as long as I'm ok." That is totally against the whole story of Chanukah. The story about Chanukah is to care and to worry about the fact that out there in the street there is somebody who is groping in the dark. If you know something about Yiddishkeit and he knows less than you, you have an obligation to share your light with him. As you know, when someone else also benefits from the light, it does not reduce your share.
There is another point: "You don't drive away darkness with a stick," as the chassidic aphorism states. The Rebbe has always emphasized that when you're trying to be mekarev another Jew and bring him closer to Yiddishkeit, you don't use a stick until he agrees to become more observant. Perhaps you will get the person to do a mitzvah by threatening him with all the dire punishments mentioned in the Torah and the writings of our Sages, but that's not the preferred way, and it is very doubtful that it will be effective. Those people who stand on the corner and throw stones and shout "Shabbos," do they really think they're going to instill in the driver a love for Shabbos, so that next Shabbos he's not going to drive? Is that really going to create a change in the number of people who desecrate Shabbos? The right way is through peace and through love and through light. "A little light dispels a lot of darkness." You just have to light a candle and immediately the darkness disappears. That's the way of Yiddishkeit. When one shines and is friendly and shares Yiddishkeit with another Jew, he will see that the darkness will melt away.