Although the demise of Nadav and Avihu occurred three parshiyos ago (in Parshas Shemini), Parshas Acharei Mos commences by referencing their deaths. Toras Kohanim, quoted by Rashi, explains that the Torah invokes the memory of the deaths of Nadav and Avihu to illustrate and emphasize the severity of the first mitzvah of the parshah - the prohibition of unlicensed entry to the Kodesh Ha-Kodoshim. The Torah's intent is to associate this prohibition with Nadav and Avihu, so as to forcefully and strikingly convey the idea that unlicensed entry is punishable by death "just as occurred to Aharon's sons". (Rashi on Vayikra 16:1-2 from Toras Kohanim 16:3)  

Although Rashi invokes the connection of the demise of Nadav and Avihu to the lav (the prohibition) of unlicensed entry to the Kodesh Ha-Kodoshim, explanation of another issue is needed:

In Parshas Shemini, immediately after Nadav and Avihu perish, the Torah commands that one may not serve in the Mishkan or Beis Ha-Mikdash while intoxicated. Midrashim explain that this prohibition is featured in conjunction with the deaths of Nadav and Avihu because (according to some interpretations) their sin was that they entered and served in the Mishkan while intoxicated. (See Targum Yonasan ben Uziel on Vayikra 10:9.) Thus, similar to what we find at the beginning of Parshas Acharei Mos, the Torah associates a lav with the deaths of Nadav and Avihu in order to emphasize and illustrate the severity of the lav.

The question that arises is why does the Torah not also feature the prohibition of unlicensed entry to the Kodesh Ha-Kodoshim back in Parshas Shemini, immediately after the demise of Nadav and Avihu, as is done with the lav of serving in the Mishkan or Mikdash while intoxicated? Why does the Torah delay the lav of unlicensed entry to the Kodesh Ha-Kodoshim until Parshas Acharei Mos?

The first section of Parshas Acharei Mos deals with Avodas Yom Ha-Kippurim, the Yom Kippur Service. We read in the parshah, as per the explanations in the Mishnah and Gemara, that the Kohen Gadol entered the Kodesh Ha-Kodoshim four times on Yom Kippur, and how he performed the extremely difficult and awe-inspiring Avodas Ha-Ketores (Incense Service) and other Avodah therein, concluding with a fervent tefillah before concluding his initial entry. The entire scenario is captivating and exhilarating; one who reads about it is gripped by the tension and the delicateness of this Avodah, which is in large part due to the ultra-sensitive location of the Kodesh Ha-Kodoshim, where it occurs.

This is precisely the reason that the lav of unlicensed entry to the Kodesh Ha-Kodoshim appears at the beginning of Parshas Acharei Mos, as part of the Avodas Yom Ha-Kippurim, rather than in Parshas Shemini. In order for one to truly appreciate the flavor and import of the Avodas Yom Ha-Kippurim, and in order for the Avodah to itself be infused with such meaning, the lav of unlicensed entry to the Kodesh Ha-Kodoshim and the heavenly death sentence that it precipitates must be a central part of the picture. Absent the knowledge that the Kodesh Ha-Kodoshim is the holiest place on earth and that entry therein without permission is a gravely severe transgression that invokes lethal consequences, the Yom Kippur Service would be lacking. As much as the Service's content is critical, so it its context. Only when the Kohen Gadol realizes and is awed that he is standing in a location of such intense kedushah and sensitivity is his Avodas Yom Ha-Kippurim elevated to the level of intensity and holiness that it must embody and represent. This is why the prohibition of unlicensed entry to the Kodesh Ha-Kodoshim appears in Parshas Acharei Mos as the introduction to the Avodas Yom Ha-Kippurim rather than in Parshas Shemini. 

On a broader scale, when performing any mitzvah, we need to view our actions from the perspective of that mitzvah's unique contextual requirements. One may not daven in the presence of nudity, offensive odors, rotting material or in a place of levity. The basis for this is that when davening, one must realize that he stands before God, and one cannot be in His presence when the context is contradictory to encountering the Shechinah. Tefillah is not merely saying words to Hashem; tefillah is standing before Him, and one must realize this and have a proper context for it.

So, too, when we learn Torah, we must realize that we are engaged in a most holy activity and are also interacting with God. This is evidenced by the requirement to rise in the presence of a talmid chochom, as he is a bearer of the holiness of the Torah. One may likewise not learn Torah in the presence of nudity, offensive odors, rotting material or in a place of levity. By looking to the contextual requirements of mitzvos, we can enhance their performance and adhere to Hashem's Law according to both its letter and spirit.