Chachma, bina vaadat. Whats the difference?

Question

Whats the difference between the concepts: chachma, bina and daat? We see them listed together in the amida.

Answer 1

On a simplistic level, Chochmah is Wisdom. It is an ability or attribute of a person. Bina is Understanding. It is the use of Chochmah to understand something. Daas is Knowledge. It is the acquired idea that one has understood with Chochmah through Binah.

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But this isn't Hebrew.SE! You want a Jewish Theology answer, else you wouldn't have used the term "concepts."

According to Chabad Chassidus, (which is itself an acronym of Chochmah, Bina, and Daas) the explanations are as follows.

• Chochmah is a spark, it is the first flash of an idea. For example, sometimes one is struggling over a problem and they get a flash of inspiration, a "Eureka" if you will. If their friend were to say, "Ok, now explain it to me", the response would be, "Give me a second, I need to think about this." It's undeveloped and unrealized. To quote Chabad.org

  Because it is as yet amorphous, comprehension is lacking; the flash of illumination might indeed be dissipated unless it is promptly developed. But already the thinker experiences delight; he is aware of a great accomplishment.

• Binah is step two. It is the expansion and the development of Chochmah's spark.

  [It] takes this concept-nucleus, examines it and develops it in all its ramifications and details.

  Binah is accomplished through contemplation and concentration.

• Daas is the conclusion. It is the application of the concept or idea that one has contemplated.

  [It] carries the idea to its logical conclusion. The conclusion will vary with the type of subject—a verdict in legal problems or an emotion consonant with the idea [...]

Answer 2

Rashi explains the difference as follows (Shemos 31:3):

וָאֲמַלֵּא אֹתוֹ רוּחַ אֱלֹהִים בְּחָכְמָה וּבִתְבוּנָה וּבְדַעַת וּבְכָל מְלָאכָה - And I have imbued him with the spirit of G-d, with wisdom, with insight, with knowledge, and with [talent for] all manner of craftsmanship

with wisdom: [I.e.,] what a person hears from others and learns. -[from Sifrei Deut. 1:13]

with insight: With his intellect he understands other things based on what he learned. -[from Sifrei Deut. 1:13]

with knowledge: The holy spirit.

Chochma refers to those things he directly received from others. Binah means applying what he learned to understand new things, and Daas is Ruach Hakodesh.

Answer 3

R' M. Mishkelov, a talmid of the Grah, explaining the verse in Mishei בחכמה יסד ארץ כונן שמים בתבונה, says the following (found in the perush haGra"h on Mishlei):

Chochma is the Torah as it is - the givens. Chochma is unchanging and constant, therefore it corresponds to ארץ because אין כל חדש תחת השמש, and similarly a Navi is not allowed to create a new Mitzvah, because the chochma of the Torah is unchanging. Therefore יסד is past tense, because it happened in the past.

Binah is the contemplation and understanding that an individual has of that information, the way he personally relates to it. It is therefore constantly changing as generations come and go. Thus, corresponding to binah, כונן is present tense, and is matched with שמים which is מחדש בכל יום (I do not know how he knows that "mechadesh b'tuvo b'chol yom" refers to shamayim and not aretz, but I assume it is because otherwise it would contradict "ein kol chadash tachas hashemesh").

This seems to match Rashi's explanation (quoted in an answer above) that chochma is what you learn from others (the information) and binah is extrapolating your own deductions.

He does not explain what Da'as is, but Nefesh Hachaim, also a talmid of the Gra"h, explains (Sha'ar aleph perek 6) that da'as is connection - which would mean that da'as is becoming connected to the information.