Parashat Korach is contained in Bamidbar (Numbers) Perek Tet-Zayin (Chapter 16) through Perek Chet-Yud (Chapter 18).

The primary focus of the Parashah is on the rebellion by Korach and his followers.  The essence of the story is that Korach insisted that Moshe (Moses) was not the only person to speak directly to God or to offer incense and decided that each member of Klal Yisrael (the Nation of Israel) was entitled to the same rights and privileges as Moshe and Aharon (Aaron).  As can be expected, Hashem did not take kindly to the uprising and destroyed all those that were a part of it.

In conclusion to this episode, God commands the following in Perek Yud-Zayin (Chapter 17):

5. as a reminder to the Children of Israel, so that no alien who is not of the offspring of Aaron shall draw near to bring up the smoke of incense before Hashem, that he not be like Korach and his assembly, as Hashem spoke about him through Moses:

In the very next verse, we see the beginning of an episode that defines a change in the relationship between God, Moshe Rabbeinu (our Rabbi Moses), and Klal Yisrael.

6. The entire assembly of the Children of Israel complained on the morrow against Moses and Aaron, saying, "You have killed the people of Hashem!":

7. And it was when the assembly gathered against Moses and Aaron, they turned to the Tent of Meeting and behold! the cloud had covered it, and the glory of Hashem appeared:

8. Moses and Aaron came before the Tent of Meeting:

9. Hashem spoke to Moses, saying:

10. "Remove yourselves from among this assembly and I shall destroy them in an instant!" They fell on their faces:

11. Moses said to Aaron, "Take the fire-pan and put on it fire from upon the Altar and place incense -- and go quickly to the assembly and provide atonement for them, for the fury has gone out from the presence of Hashem; the plague has begun!":

12. Aaron took as Moses had spoken and ran to the midst of the congregation, and behold! the plague had begun among the people. He placed the incense and provided atonement for the people:

13. He stood between the dead and the living, and the plague was checked:

Up until this point, Moshe was able to intercede and beg for forgiveness on behalf of Klal Yisrael.  With the rebellion of Korach, that is no longer possible.  It would appear that we have an instance of, "Be careful what you wish for…"  With Korach insisting the people had a right to communicate directly with Hashem, this is now a part of the relationship.  What Korach and the people did not understand is that, such an association has responsibilities more than privileges.  Without assuming the responsibilities, the consequences can be devastating.

Rav Hirsch says:

This accusation [by the people] was certainly a purely personal reproach, as a result of which God said to Moses:  If you wish it, get yourselves up out of them and I will immediately make an end of these masses that rise up against you.  But they did not move, on the contrary, threw themselves down on their faces before God; and instead of going away from the people -- instead of demanding the death of their offenders as a penalty, like the deaths which the accusing masses fathered on them, calling them "bringers of death to the people of God" -- Aaron had to rush into the midst of the nation condemned to death, and with the [incense] rising up to God, the symbol of the most complete giving oneself up to God, place himself between the dying and the living, making atonement for them and proving himself and his mission, contrary to their accusation, the redeeming conqueror of Death.  

In this instance, Moshe and Aharon demonstrate the essence of Judaism - Ahavat Yisrael - a love for Klal Yisrael and all the people within it.