HaShem commands the Jewish people: "An eternal flame should always be kept burning on the altar; it should never be extinguished."
The fire on the mizbeach (altar) where the sacrifices were offered should always continue to burn. In the Beis HaMikdash, there was a special chamber where hot coals were kept alive, so that the fire on the mizbeach could be relit whenever necessary.
This mitzvah has an especially deep meaning today, as we prepare for the Third Beis HaMikdash.
When HaShem commanded the Jewish people to build the mishkan, He said: "And I will dwell within them." Shouldn't the possuk have said "I will dwell within it"? It says "them" to teach us that every Jewish person is like a miniature Beis HaMikdash. Every Jew must always have a fiery love for HaShem in his heart, just like the fire which burns all the time on the altar.
In the Talmud, our Rabbis teach us more details about this mitzvah: The fire on the altar was to be kept burning even on Shabbos and even b'tumah, when we are impure.
In the same way, we Jews should always feel a deep love for HaShem, whether we are on a level of Shabbos or on a level of tumah.
What do we mean by "a level of Shabbos"?
On Shabbos, we wish each other Shabbat Shalom. The Hebrew word Shalom comes from the root shaleim, meaning whole and complete. We feel complete on Shabbos. We relax and we do not worry about our weekday work, acting as if it were completed.
On Shabbos, we are also given an extra Shabbos neshamah that helps us daven better, learn better, and understand HaShem's holiness better. But a Jew on the level of Shabbos might only pay attention to his learning and understanding, and he might ignore his feelings. So HaShem reminds him of the "eternal flame... even on Shabbos." The burning love for HaShem in our hearts should never relax.
Then our Rabbis add, "even when impure." Even if a Jew is impure, he should dig deep into his heart and bring out the love for HaShem which is always there.
(Adapted from Likkutei Sichos, Vol. I, Parshas Tzav)