Achrei means "after," as in the opening verse of our Parsha: "God spoke to Moshe after the death of Aharon's tow sons - when they came near, before God, and they died."
Chasidic thought explains that Aharon's sons did not die because they where wicked and transgressed God's will. Rather they where righteous individuals who wanted to come closer to God. But this yearning became so strong that it reached the point where they no longer wished to continue a normal, bodily existence, which makes a person feel distant from his Maker, and they simply expired. Thus, the verse actually describes the cause of their death: "they came near, before God, and - therefor - they died."
At first glance, it might appear that the yearning of Nadav and Avihu to come close to God was misplaced, as God clearly dose not want us to die out of love for Him.
In truth however, Nadav and Havihu's desire to come close to God and leave their bodily existence, was entirely appropriate to have - on a temporary basis. Their fault was in their inability to redirect those energies back into normal, everyday life, after a period of heightened spiritual arousal.
In other words, if a person does not have times when he simply wishes to leave the confines of corporeal existence and come closer to his Maker, than that person is lacking a certain spiritual sensitivity. But, on the other hand, when a person does have these feelings he most eventually come to the realization that God placed him in this world for a purpose which necessitates his soul remaining in his body. The harmonious fluctuation of these tow opposite emotions is thus the sign of a healthy spirituality, rather like the rhythmic beating of the heart is a sign of physical wellbeing.
So, the intense spiritually of Nadav and Avihu was actually a good thing from which we should all learn. The fact that they failed to channel their love of God back "down to earth" was indeed a fault, but that does not mean that we cannot learn from their positive qualities.
And it is precisely for this reason that the Parsha is called Achrei ("after"). For Nadav and Avihu were the first individuals (record in the Torah) to demonstrate an intense spiritual yearning, which set a new precedent for all Jewish people as to what levels of emotional attachment to God could be achieved. Thus, "after the death of Aharon's tow sons," the Jewish people entered a new era where higher standards of spirituality had been set.
(Based on Sichas Shabbos Parshas Achrei-Kedoshim 5750)