Frequently, when Tanac"h speaks about a man and woman having sexual relations, it uses the term ידע as in Breishit 4:1
וְהָ֣אָדָ֔ם יָדַ֖ע אֶת־חַוָּ֣ה אִשְׁתּ֑וֹ וַתַּ֙הַר֙ וַתֵּ֣לֶד אֶת־קַ֔יִן
The verb also means "to know". Why is the term for "knowledge" used? Is there some type of knowledge that is gained via sexual relations, and what knowledge is that?
Ibn Ezra to Genesis (3:6) suggests that Adam had sex with Eve as a result of eating from the Tree of Knowledge. Therefore, sex is euphemistically referred to as knowledge. Additionally, he notes that the sex drive develops as a person becomes aware of good and evil; further reason for the euphemism.
Radak to Genesis (4:1 (3:20)) seems to imply this as well.
In addition to associating sex with the Tree of Knowledge like Ibn Ezra, Rabbenu Bahya to Genesis (4:1) and Tol'dot Yitshak (Genesis 4:1) of R. Yitshak Karo explains it based on the ancient Greek belief (see here) that semen comes from the brain. Accordingly, sex is associated with cognition. This latter explanation is given by R. Avraham Saba in Tsror HaMor to Genesis (Parashat Vayeshev s.v. V'haadam Yada) as well.
Malbim to Genesis (4:25) writes that the term 'knowledge' is generally found in scripture in the context of a couple's first sexual encounter. The connection would therefore be that they gain a new degree of intimacy and knowledge of each other.
HaKtav V'HaKaballah to Genesis (4:1) cites some who explain that the knowledge refers to the man's perceiving the woman which arouses him. He proposes a different explanation; that (if I understand him correctly) it is related to the term יעד, meaning connecting or designating. R. Yehoshua Ibn Shuaib (Drashot R”I ibn Shuaib, p. 48 column 4) similarly explains the expression connotes connection. He quotes this explanation from Ibn Ezra, but I am not aware of anywhere that Ibn Ezra says this. The idea of the expression denoting connection is also stated by Rabbenu Avraham ben Sh'lomo in his commentary to I Samuel (pg. 17), and the Shelah (Pesahim: Perek Torah Ohr: 134).
This is later repeated in Hassidic literature such as Ben Porat Yosef (Parashat MiKets s.v. Ubazeh Yuvan), Noam Elimelekh (Parashat Shelah s.v. yomar), Ohev Yisrael to Shemot (Parashat Parah s.v. V'yikhu Elekha), Siftei Tsaddikim (Ketuvim s.v. Bapassuk ki), and B'Nei Yissakhar (Maamarei Rosh Hodesh Maamar Aleph - Kiddush HaHodesh s.v. heh).
R. DZ Hoffman writes in his commentary to the verse that it means to perceive with the senses (I assume this is the idea quoted above from HaKtav V'HaKabbalah) and is a euphemism for sex. He notes that similar usages are found in Greek and Latin.
Haamek Davar to Genesis 4:1:
It's worth knowing that, wherever "know" is used when discussing sexual intercourse, its intent is that he recognized and knew whom he was with, and [that he was with her] because she was that woman and not another; this is along the lines of kidushin.… That the wording "he knew" is used by Elkana and Chana in I Samuel [1:19] intends that, because he knew that from this act with Chana specifically would a great and holy man be produced, he prepared more at the time of intercourse: thus, "he knew" which woman he was with [and had intercourse with specifically her].
To 4:25 ("Adam knew his wife again" and she had Seth), he comments, offering two explanations for "knew": According to the midrash that Adam and Eve had separated for years, this was a copulation for remarriage and thus designating a mate. Otherwise, it's because the other kids they had had meanwhile were not worth mentioning whereas Adam knew that this one would be an important man so he prepared specifically for copulation with the one woman who was fit to produce such offspring.
Nefesh HaChaim שער א פרק ו writes that da'as means connection:
כי דעת פי' התחברות כידוע
...as the meaning of da'as is connection, as is well-known
(Not to get over-involved in this point, but this is concept shows up in many places. For example, da'as is the connection of chochma and binah, dibbur (speech), which comes from da'as, is the connection of sechel and ma'aseh, and comes from the ru'ach, which is the connection of the neshama and the nefesh/guf.)
Therefore, explains the Nefesh HaChaim (ibid) that eating from the Etz HaDa'as caused a connection (and a mixing) within Adam of the capacity towards good and evil, whereas prior to his sin evil had been something external to him.
Based on this understanding, I think it could be understood that sexual relations are referred to as da'as as they are the connection between man and woman, which actually "mixes" them into a new entity as they become לבשר אחד, one flesh.
(There is a Maamar of the Lubavitcher Rebbe related to why the eagle is so special (kabolisticly) and explains that it is in the middle line (chohmo, gevura... is on the right. bina , gevura... is on the left, but das, tifferes and yeaod (also known as the male organ) is in the middle))
Where he also brings as evidence that the middle line goes directly non stop that right when a person is aroused in his daas in his brain, his yesod is awakened (he gets an erection),
Melukat 1 haazinu 5729 by footnote 25)
(in other places it is explained that, since having children is the opposite of entropy, it is a miracle so high levels of G-dliness is needed to produce them)
Yevamot 53b
אין קישוי אלא לדעת
there is no erection of the male organ without (daas) intent
So I guess it is used because it is a clean word, and it can be used to refer to relations, since it is a necessary part of it
(it is not considered relations if no erection and no erection is possible without daas (above))
So I do not think knowledge is gained from relations, it is only that knowledge is necessary to have them (a child does not have complete daas, he starts from almost 0 and he can not have relations until he gains it slowly by 9 or 13 years old)
