In his search for a place to bury his late wife Sarah, the Torah  tells us how Avraham asked the Hittites to sell him "the cave of Machpelah (duplication)" for that purpose. Rashi quotes the word "Machpelah" and says: "A house with an attic".
At first sight it seems that Rashi's intention is to explain that the cave was called Machpelah ("duplication") because it was "double", in other words, it consisted of two caves, one above the other.
But, it is not all that simple:
"Double" only implies that there are two. How does Rashi know that the two caves were situated one above the other and not one within the other?
"Double" implies that we are dealing with one thing that is composed of two. It would therefore be more logical to say that the two caves were inside one another and not one above the other, since when one cave is within the other, they are interdependent (you must enter the outer cave in order to reach the inner one), unlike in the case of one above the other.
Houses and caves are two very different concepts, indeed opposites. A house is usually built above ground, as opposed to a cave that is generally below ground. Why does Rashi use an example of a house and attic to explain the concept of "double" instead of saying directly: one cave on top of the other?
Rashi continues in his commentary: "Another explanation: because it was duplicated in pairs." (As Rashi explained earlier , Adam and Eve, Avraham and Sarah, Yitzchak and Rivkah, Jacob and Leah were buried there).
We need to understand: What was the purpose of mentioning in his conversation with the Hittites that he wanted the cave because four couples would be buried there? By mentioning the special value of the plot, its being the burial place of Adam and Eve as well as the future progenitors of the Jewish people, would it not cause Ephron to raise the price of his property?
Another question: we see from the text in the verses below ("The field of Machpelah" ; "the cave of the field of Machpelah" ) that the adjective Machpelah —"double"— does not necessarily refer to the cave but to the field in which the cave was located. Why does Rashi see the need to explain the significance of the name altogether, being that Rashi does not generally explain the meaning of biblical names unless the explanation of the meaning of the name clarifies a difficulty in the understanding of the text? And, if Rashi sees the need to explain it, why does he explain it as an adjective that describes the characteristics of the cave itself, even though we see that it also refers to the field itself?
Given that in our verse the adjective machpelah ("double") comes immediately after the word Mearat ("cave of") —"Let him give me the cave of Machpelah that belongs to him [located] on the edge of his land"— it is understood that it refers to the cave itself and not to the field in which the cave was located.
However, since we later see in the text that the entire field was also called the machpelah field, it is understood that the adjective referred neither to the cave nor to the field, but rather to something located in the field and near the cave, namely: a house with an attic.
Also: since a "double" cave would imply something more important than a simple cave and Avraham wanted to diminish its importance, as we can see by the fact that he refers to it as the cave that is "on the edge of his field", it is logical to say that the adjective does not describe the cave but is a reference to its location (which ended up giving the name to both the cave and the field in general).
Why, then, is Rashi forced to give a second explanation, that "machpelah" implies that it is a plot that can accommodate several couples?
We see in the text  that the Hittites offered Avraham "the most select of our burial grounds" to bury Sarah. What would the justification be for asking for a less important plot, which is situated on the edge of the property?
It is to clear up this doubt that Rashi says that Machpelah also implies "couples". The implication is that Avraham told them that he prefers that plot rather than "the most select" because he was looking for a plot not only to bury his wife Sarah, but to serve as a family plot that would be used for himself, his son and grandson as well as their spouses.
The mystical dimension:
The Zohar explains that the word hamachpela also implies "Hei machpelah" or "double Hei", referring to the two letters Hei in G-d's name. The Tzemach Tzedek explains that the "house with a loft" to which Rashi refers represents these two letters: the "house" represents the lower Hei and the "loft" represents the upper Hei.
What do the two letters Hei have to do with the Machpelah Cave itself?
The mission of the soul in this world is to achieve Teshuvah, since before descending to this world one is at the level of Tzaddik (just). There are, however, two levels of Teshuvah: "lower" Teshuvah and "higher" Teshuvah. In the founding text of Chabad, the Tanya, it is explained that the structure of the word Teshuvah, "return", also implies "Tashuv Hei", meaning "to return the Hei", referring to the soul whose spiritual origin is represented by the letter Hei of G-d's name. In fact, there are two letters Hei that represent two levels of Teshuvah: 1) turning away from evil and 2) coming closer to G-d. The maximum level of reconnection with G-d is achieved when the soul detaches itself from the body. The patriarchs and matriarchs buried in Mearat Hamachpelah represent this maximum level of connection.
Each of the two general levels of Teshuvah has, in turn, two movements, "ascent" and "descent", elevating oneself to a higher level and bringing he higher levels down to the lower levels.
These two definitions of Teshuvah —the two general ones and the two dynamics within each category— are insinuated by Rashi's two explanations:
"A house with a loft" implies the two steps of Teshuvah, the "basic" and the "advanced". Just like in the case of a house with a loft, the loft can exist only if there is a solid ground floor, the superior level of Teshuva (teshuvah ilaah) can exist only after one has achieved the basic level of Teshuvah (teshuvah tata'ah).
"Double in pairs" represents the two dynamics —male (descent) and female (ascent)— present in each of the two levels of Teshuvah.
Based on Likutei Sichot vol. 5, pp. 105-111