A Daf Yomi Shi'ur that I listen to went into details about Hechsher Mitzvah when we reached Yevamoth 6a.
Essentially, Rashi says that the Gemara's term, "Hechsher Mitzvah", is referring to a scenario in which the Mitzvah can only be fulfilled by violating a prohibition.
Tosafoth, on the other hand, explains that it means doing prohibited actions that enable the later fulfillment of a Mitzvah.
The Gemara's aim here is to find out if there is a difference between various types of Mitzvoth when it comes to the question of whether a positive obligation will override a prohibition, and, as far as I can tell, the examples chosen (a Kohen whose father tells him to retrieve an object from a cemetery; any person whose father tells him to slaughter and cook an animal for him on Sabbath; someone who wants to build the Beith HaMikdash on Shabbath; among others) can fit with either interpretation. Per Tosafoth, those actions do not immediately fulfill any Mitzvah - they enable later Mitzvah fulfillment (giving the retrieved object to the father, feeding the father, bringing sacrifices). Per Rashi, though, they are Mitzvoth themselves, and they cannot be fulfilled without directly violating a prohibition.
For some reason, the teacher of the class calls Rashi's approach "shver" (strange), and says "we learn like" Tosafoth.
Granted, as far as I know, the interpretation of Tosafoth is the more common use of this term (that is, "Hechsher Mitzvah", when I encounter it, usually means that your actions right now enable later performance of Mitzvoth). But what's so "shver" about Rashi here?